Unscoped (Episodic) Logical Forms

Some Thoughts on the Atemporal/Temporal Distinction

2019-01-10T00:00:00-08:00

TODO: add the FOL** distinction to the document since that problem still exists. TODO: ask Len about the distinction between situations, events, and episodes with regard to the EL ontology. Are they equivalent? Or is there some amount of subtlety to it that led him to say that types are D->E->2 rather than D->S->2? If they’re equivalent, I’m not sure which name I prefer. I like that situation is most distinct from stuff like Davidsonian semantics, but I suppose there’s situation semantics that we’d clash terms with. Also, since we have event variables, maybe we should just call them events? Just make it clear that due to the underlying theory, it’s not the same as Davidsonian events (I remember seeing somethign like this already in the document). TODO: we should probably still have a distinction between adv-a as an action modifier and one for a predicate modifier. Since the type for an action is (D,E)->2, and a predicate modifier is (D->S->2)->(D->S->2).

NB: Although this post is written be me (Gene), it’s based on discussion with Len, and honestly most of these ideas are from Len. BUT, any postitions taken in the post are mine, not Len’s.

Up to this point we’ve been thinking of the temporal/atemporal distinction in EL as being roughly equivalent to Greg’s stage-level vs individual-level predicates and been formalizing the atemporal distinction in EL in the following ways.

For FOL** (FOL-like subset of EL)

atemporal: \(\mathcal{D}^n \rightarrow \mathcal{2}\)
temporal: \(\mathcal{D}^n \rightarrow (\mathcal{S} \rightarrow \mathcal{2})\)

That is, atemporal predicates take individuals and return a truth value, whereas temporal predicates need to also be supplied a situation, which is associated with a temporal timespan, to return a truth value.

For EL (as currently proposed at the time of writing)

atemporal: \(\mathcal{D}^n \rightarrow (\mathcal{S} \rightarrow \mathcal{2})\)
temporal: \(\mathcal{D}^n \rightarrow (\mathcal{S} \rightarrow \mathcal{2})\)

That is, all predicates take a situation in order to return a truth value. This is done with a trick of saying that atemporal sentences characterized empty situations. So atempral predicates take \(n\) individuals and return either \(0_\epsilon\) or \(1_\epsilon\), where these functions respectively return \(0\) and \(0\) when applied to \(\epsilon\), the empty situation, and are otherwise undefined. So this captures timelessness of atemporal predicates while still having the same type. From the position of ULF, then we don’t actually need to make a distinction between these two things.

However, in making this distinction, Len and I both had the thought that perhaps all nouns (and maybe even adjectives) are in fact atemporal but then the copula acts as a mediator to turn this into a temporal statement. Given this sort of analysis human.n is atemporal so (|John| human.n) means that the individual is timelessly human whereas(|John| ((pres be.v) human.n)) is temporal and may only be true for a limited segment of time. This may seem a bit ridiculous, but it’s based on some examples that Greg has brought up before, where seemingly temporal nouns are allowed outside of their intuitively restricted temporal span. For example,

“After an emergency landing of the plane this morning, all the passengers are now safely at home.”

Strictly speaking, they are no longer passengers, but this is still an acceptable sentence. So it seems then, that nouns are in some sense timelessly true, but pragmatically non-sensical in certain contexts. It turns out that this approach comes across some problems.

As defined, there aren’t very many atemporal predicates in natural language.
Once we look more closely, we find that the temporal/atemporal distinction we’ve made isn’t really the same thing as what Greg what getting at in the individual- and stage- level predicates.
Considering nouns to be atemporal – turned temporal via the copula – is untenable when considering other syntactic contexts in which nouns appear.

There are other approaches that allow us to handle nouns taht seem to be referenced outside of their temporal restricted context, without resorting to treating nouns as atemporal. This in combinations with the problems that I listed seem to indicate that there’s a better, simpler alternative. Well, simpler for the ULF project. Now, I’m going to go into each of what I said in more detail.

Atemporal Predicates in Natural Language?

So truly atemporal predicates seem to basically be non-existent in natural language. Perhaps abstract notions like mathematical classes (e.g. number.n, even.a, odd.a, set.n) can be atemporal, but all things in the world are temporally bound in their existence. We’ll need to make sure that if we’re treating many predicates as atemporal, that some mechanism ensures that the real-world temporal restrictions are somehow maintained.

Atemporal/temporal vs stage/individual

At first glance it would seem that the atemporal/temporal distinction is doing the same thing as stage/individual level predicate distinction right? Afterall, if a predicate is true of an individual over its lifetime, then it’s basically atemporal, that is true of that individual at all times.

However, individual level predicates aren’t necessary unchangeable. It’s simply that they are longer-term and there are differences in acceptability of syntactic contexts that reflect these differences. I’ve already mentioned one of the differences, which is with individual level predicates can be used to refer to an individual even when it doesn’t seem to hold anymore. So even though we can have a sentence like “Bob is a student now, but won’t be a student next year” indicating that it’s changeable we also have sentences like “The student is now a doctor”, where presumeably, the student is not continuing to be a student while practicing as a doctor. This seems to show that in some way “student” can still be truthfully applied to this individual.

I mentioned already that we may consider this to be handled via the copula. So in “Bob is a student now, but won’t be a student next year”, “student” is atemporal, BUT “is a student” is not. But what happens in uses without a copula like appositives? *“John, a student, already graduated” is not acceptable, and there’s no copula there to make it temporal. So the copula handling doesn’t seem to be able to capture all the cases where these atemporal predicates are being used with temporal restrictions.

Other than examples like these, it

TODO: finish this…

I agree that we probably can’t maintain that the temporal/atemporal distinction corresponds to the stage/individual level predicates, I’m not sure if it’s completely untenable to maintain the temporal/atemparal distinction with the copula as the mediator between the atemporal and temporal uses of a noun. That is, the predicate “student” is atemporal, but when used with the copula has a temporal restriction. All the quantification examples would be handled by this from the fact that due to the predicates being atemporal (and without a copula), the temporal relationship between when it actually holds for the restrictor and the time of the matrix is not relevant since the semantics don’t say anything about when it actually holds for the restrictor. Arguably, this approach can explain the issue with

“The fugitives crying for joy are now in jail”

Since “fugitives” is atemporal, the actual time that this applied is pragmatically inferred, whereas “crying for joy” is temporal, so it gets tied to the matrix. This also seems to explain the two readings of “crying fugitives” in

“The crying fugitives are now in jail”

Either we get a reading similar to the above example where “crying fugitive” is read intersectively and thus “crying” is tied to the matrix predicate time. Or we get “crying fugitive” as a specific type of fugitive, where “crying” is non-intersectively modifying “fugitives”. Then the “crying” time is independent of the time of the matrix event. I can imagine either an instance where the fugitives, whenever they were spotted, were crying so they got dubbed “the crying fugitives” or a case where during a particularly noteworthy event, the fugitives were crying so they got dubbed “the crying fugitives”.

I think all the other examples you gave could be handled with the copula-assisted temporal interpretation of atemporal predicates. Perhaps this is an unsatisfying analysis though, in which the temporal relationship between the actual time when the restrictor predicate applies to the individual is ignored on a technicality and then resolved using pragmatics and world knowledge. For example, the creation/ destruction examples reduce knowing that most predicates, including individual level nouns aren’t

This really seems to be an issue of nouns though, not all individual level predicates since we can’t quantify over individual predicates that aren’t nouns (e.g. the loyal are here -> the loyal (people) are here).

The biggest problem with this approach to me seems post-nominal modifiers that clearly restrict the temporal scope without using the copula. *“John, a student, already graduated” is not acceptable, and there’s no copula there. We would have to interpret appositives as having an elided copula in order to get the right meaning. This isn’t impossible, but it seems messy. This isn’t to say that I think this approach is what we should do. I just don’t necessarily think it’s impossible to maintain this approach.

I’m not sure if we should talk about the temporal-atemporal distinction at all. If in EL the types are unified into a single type, then why should we make a distinction in ULF?

Considering this, I think we should clean up our predicate modifiers. First of all, I want to make a distinction between action modifiers, e.g. manners, adjective modifiers (e.g. very happy) since the latter really aren’t action modifiers and seem to be a different semantic type. Furthermore, I want to either fully incorporate the syntactic types to the type system or not at all. So either, have one predicate modifier forming type (and eliminate attr, nn). or fully distinguish them (e.g. adv-adj, adv-v, kind of thing). It just seems really strange to me that we make the effort to distinguish ‘nn’, from ‘attr’, but then all the other predicate modifiers are formed using ‘adv-a’.

Modification in ULF

2019-01-09T00:00:00-08:00

Prerequisite Knowledge

Understanding the crux of this post requires

basic knowledge of EL semantic types and associated notation,
basic knowledge of ULF syntax,
basic knowledge of the EL interpretation process,
familiarity with English syntax terminology, and
familiarity with terminology such as ‘predicate’ and ‘intensional’ from logic.

Some details also require knowledge of

Skolemization,
lambda functions, and
the EL charaterizing operator **.

Predicate Modification

EL semantic types represent predicate modifiers as functions from monadic predicates to monadic predicates, i.e. (\((\mathcal{D} \rightarrow \mathcal{2}) \rightarrow (\mathcal{D} \rightarrow \mathcal{2})\)). This enables handling of non-intersective modifiers, e.g.nearly, fake, almost. These are further distinguished by the syntactic category of the predicate being modified.

noun modification: (fake.mod-n diamond.n)
adjective modification: (very.mod-a happy.a)
verb modification: (nearly.adv-a fall.v)

So the type extensions .mod-n and .mod-a are noun and adjective premodifier types, respectively. .adv-a is the VP adverbial type, which corresponds to monadic verb modifiers. Ultimately, these become action modifiers in EL semantics, hence the -a extension. Since actions aren’t explicitly represented in ULF, .adv-a modifiers are represented as intensional monadic verb modifiers. (See Actions, Experiences, and Attributes for more details).

There are type-shifters that form operators of each of these types from monadic predicates. The operator names borrow from the extensions that accompany the lexical versions of these modifiers. So mod-a, mod-n, and adv-a (note, no dot preceding them) are type-shifters that shift monadic predicates to adjective modifiers, noun modifiers, and VP modifiers, respectively. Here are some examples

((mod-n wooden.a) shoe.n), ((mod-n ice.n) pick.n), (fake.mod-n ruby.n),
((mod-n worldly.a) wise.a), (very.mod-a fit.a), (slyly.adv-a grin.v)

In English there’s also common noun premodification by a proper noun, e.g. “Seattle skyline”. For this case we also introduce a type-shifter from a proper noun to a nominal modifier, nnp.

((nnp |Seattle|) skyline.n)

Here is a table of each of the type-shifters introduced so far along wth an example and the formal type.

Table of Predicate Modifier Forming Operators

Name	Example	Formal Type
`mod-a`	`((mod-a worldly.a) wise.a)`	\(\mathcal{N} \rightarrow ( \mathcal{N}_{ADJ} \rightarrow \mathcal{N}_{ADJ} ) \)
`mod-n`	`((mod-a (very.mod-a happy.a)) dog.n)`	\(\mathcal{N} \rightarrow ( \mathcal{N}_{N} \rightarrow \mathcal{N}_{N} ) \)
`adv-a`	`(play.v (adv-a (with.p (a.d dog.n))))`	\(\mathcal{N} \rightarrow ( \mathcal{N}_{V} \rightarrow \mathcal{N}_{V} ) \)
`nnp`	`((nnp \|Seattle\|) skyline.n)`	\(\mathcal{D} \rightarrow ( \mathcal{N}_{N} \rightarrow \mathcal{N}_{N} ) \)

Since in ULF there are no valid adjective-adjective, adjective-noun, noun-noun, noun-adjective compositions without this sort of type-shifting, we can often omit mod-a and mod-n type-shifters and introduce them in post-processing. For example, “burning hot melting pot” is hand annotated as

((burning.a hot.a) (melting.n pot.n))

which gets post-processed to

((mod-n ((mod-a burning.a) hot.a)) ((mod-n melting.n) pot.n))

Therefore, when there’s a (ADJ ADJ), (ADJ N), (N N), or (N ADJ) structure we infer that the first argument is a modifier and the second is being modified.

This cannot be done when the modifier is a verb – “running man”, “sleeping beauty”, “frequently returning member”, annotated ((mod-n run.v) man.n), ((mod-n sleep.v) beauty.n), and ((mod-n (frequently.adv-f return.v)) (member-of.n *ref)), respectively. The -ing morpheme here seems to be acting as an indication that this is a modifier, rather than marking a progressive or turning the verb into a noun. This also occurs for verb-verb modification, e.g. “He ran in the forest, looking at the trees” becomes

(he.pro 
  ((past run.v) (adv-e (in.p (the.d forest.n))) 
                (adv-a (look.v (at.p-arg (the.d (plur tree.n)))))))

The subsection on Participial Phrases discusses such verb phrase modifiers in more detail. Verbs need explicit type-shifters because some verbs can take predicate arguments so it would be ambiguous whether the noun or adjective following a verb is an argument or if the verb is acting as a predicate modifier. An example of a predicate argument is sad in “He looks sad”. sad is a predicate argument to looks in this case. This is the same reason that verb modifiers (i.e. of adv-a type) always require the type-shifter explicitly.

Notice from the examples in the table of predicate modifier forming operators that the operators aren’t necessarily prefixed in ULFs, rather they appear in the surface word order. In EL, monadic operators are prefixed, whereas operators with more arguments are infixed. In ULF, we leave them in place since the operator and operand can be inferred from the types of the constituents. Consider the types for play.v and (adv-a (with.p (the.d dog.n))). Since the former is an verbal monadic predicate and the latter is an verbal monadic predicate modifier, we can be certain that (adv-a (with.p (the.d dog.n))) is the operator while play.v is the operand.

Premodification of adjectives and nouns in English tend to allow non-intersective readings, though this isn’t always the case. The formal type of the modifiers described so far as intensional predicate modifiers (i.e. \(\mathcal{N} \rightarrow \mathcal{N}\) allows us to handle both cases. An example of and intersective reading for premodification is “triangular container” which we annotate as ((mod-n triangular.a) container.n). Since this relation is intersective, given the correct background knowledge, we would infer that this has the same meaning as (lambda x ((x triangular.a) and.cc (x container.n))). There are some constructions in English that really seem to always indicate an intersective interpretation via the grammar, for which we annotate them as such. This includes post-nominal modification and appositives. For example, we would annotate “The buildings in the city” as (see the post on macros for details of the n+preds macro)

(The.d (n+preds (plur building.n)                        
                (in.p (the.d city.n))))

which is equivalent to

(The.d (lambda x ((x (plur building.n)) and.cc
                  (x (in.p (the.d city.n))))))

Thus we distinguish grammatical constructions that indicate intersective modification, but ULFs do not distinguish all intersective vs. non-intersective modification.

Actions, Experiences, and Attributes

In the general description, we glanced over what actions – and more generally, experiences and attributes – are (i.e. what .adv-a type predicate modifiers ultimately act over in EL). Here we describe them a bit more carefully.
Adverbial modifiers of the sort .adv-a intuitively modify actions, experiences, or attributes, which are a category of individuals in the EL ontology distinct from events and situations. It’s designed to deal with semantic subtleties such as:

“He lifted the child easily” – which refers to an action that was easy for the agent, rather than to an easy event;
“He fell painfully” – which refers to a painful experience rather than to a painful event; and
“He excels intellectually” – which refers to an intellectual attribute rather than to an intellectual event or situation.

Actions, experiences, and attributes in EL are individuals comprised of agent-episode pairs and this allows modifiers of the sort .adv-a to express a constraint on both the agent (more generally, subject) of a sentence and the episode it characterizes. No sharp or exhaustive classification of such pairs into actions, experiences, and attributes is presupposed by this – the point is just to make the subject of sentences available in working out entailments of VP-modification. Since actions are derived, in part, from explicit episodes and such episodes are implicit in ULFs until deindexing, actions are also implicit in ULFs. Formally, actions have the semantic type \( \subset \mathcal{D}\), where \(\) is the range of a pairing function, pair, of type \((\mathcal{D} \times \mathcal{S}) \rightarrow \mathcal{D}\). These action-based constraints are derived from .adv-a predicate modifiers via meaning postulate inference rules. So the formula (used in the main discussion)

(|John| (play.v (adv-a (with.p (the.d dog.n)))))

after event deindexing and canonicalization could become the formula

[[|John| (play.v (adv-a (with.p (the.d dog.n))))] ** E1.sk]

where E1.sk is a Skolemized episode variable. From this we can infer

[[|John| play.v] ** E1.sk],
[(pair |John| E1.sk) with.p (the.d dog.n)]

The pairing function can also be written with the pipe shorthand, (pair X Y) \( \equiv \) [X | Y]. So the second formula above can be rewritten as [[|John| | E1.sk] with.p (the.d dog.n)]. Lexical .adv-a modifiers are similarly derived into predications over actions. “They escape quickly” (ignoring tense) has the raw ULF representation

(they.pro (escape.v quickly.adv-a))

which after event deindexing, event canonicalization, and .adv-a inference results in

[[they.pro escape.v] ** E1.sk] and [[they.pro | E1.sk] quick.a]

Note the conversion of quickly.adv-a to quick.a, since a predication over actions is inferred from the verb modification.

Participial Phrases

In case you’re unfamiliar, partiples are verbs are used as adjectives (working woman, running man) or nouns (the exquisite cleaning). As you may have noticed, for simple cases we simply change the suffix marking of the word to the POS that it is acting as; e.g. (working.a woman.n), (running.a man.n), and (the.d (exquisite.a cleaning.n)). However, for complex participial phrases, this no longer works because the verb may take arguments in ways don’t fit into formal interpretation of adjectives and nouns. Consider for example,

I greeted the frequently returning member
We’re required to submit a carefully written notice
Kenneth nervously watched the woman, alarmed by her gun
I went back to sleep, having heard this before

It seems that we can make arbitrarily complex verb phrases into paritipial phrases, including those that have passivization and perfect aspect. All cases that initially looked tensed turned out to be passivization as far as I’ve seen so far. Participial phrases also don’t allow progressives, since the -ing morpheme is already in use. It can get confusing though since in many cases participles have a concurrent interpretation, but this isn’t always the case, e.g.

Lifting weights for two hours, Ron developed sore muscles
The student scoring the highest grade on the exam will receive an award

We consider the concurrent vs. non-concurrent interpretation to be a pragmatic issue and therefore leave it ambiguous in the ULF representation of paritipial phrases.

In ULF we don’t have a single category for participial phrases since the semantic type structure can vary. When the verb is acting as a predicate modifying adjective, we will treat complex participial phrases as untensed verb phrases which may include perf and pasv which are type-shifted to the appropriate predicate modifier. For how we handle nominal participial phrases, please refer to the Derived Nominals section of the annotation guidelines. Here are some concrete examples of complex predicate modifying participial phrase annotations in ULF.

I greeted the frequently returning member

(i.pro ((past greet.v) 
     (the.d ((mod-n (frequently.adv-f return.v)) 
             (member-of.n *ref)))))

We’re required to submit a carefully written notice

(we.pro ((pres (pasv require.v)) 
      (to (submit.v 
           (a.d ((mod-n (carefully.adv-a (pasv write.v))) 
                 notice.n))))))

Kenneth nervously watched the woman, alarmed by her gun

(|Kenneth| 
  (nervously.adv-a 
 ((past watch.v) (the.d woman.n)
                 (adv-a ((pasv alarm.v) (by.p-arg (her.d gun.n)))))))

I went back to sleep, having heard this before

(i.pro ((past go.v) back.adv-a (to.p-arg (k sleep.n))
                 (adv-a (perf (hear.v this.pro before.adv-e)))))

Lifting weights for two hours, Ron developed sore muscles

(sub 
  (adv-a (lift.v (k (plur weight.n)) 
              (adv-e (for.p (two.d (plur hour.n))))))
  (|Ron| ((past develop.v) (k (sore.a (plur muscle.n))) *h)))

Any student scoring a good grade on the exam will receive an award

((any.d (n+preds student.n
              (score.v (a.d (good.a grade.n)) 
                       (on.p-arg (the.d exam.n)))))
 ((pres will.aux-s) (receive.v (an.d award.n))))

Comparison of Modifier Notation Against Stanford Dependencies

The Stanford dependency parser indicates the lexical category of the modifier, not the operand.

amod - adjectival modifier
nmod – nominal modifier
advmod – adverbial modifier
partmod – participal modifier (e.g. “recorded message”)
tmod – temporal modifier (e.g. “said today”)
etc.

If we regard their amod, nmod, partmod labels as of type monadic predicate to monadic-predicate, we have a kind of equivalence to what we’re doing for N-premodification. But the ULF notation is more informative concerning adverbs, because their advmod is ambiguous between adjective-modifying, VP-modifying and S-modifying. The their notation is slightly more informative than ULF for noun premodification – they make distinctions like premodifying (ordinary) adjective vs. premodifying participle.

Sentence Modification

A formula or nonatomic verbal predicate in ULF may contain sentential modifiers of type \((\mathcal{S} \rightarrow \mathcal{2}) \rightarrow (\mathcal{S} \rightarrow \mathcal{2})\): divided corresponding to their EL semantic differences into sorts .adv-s, .adv-e, and .adv-f. Again there are type-shifting operators that create these sorts of modifiers from monadic predicates. Sentential modifiers of the sort .adv-s are usually modal (and thus opaque), e.g.,

perhaps.adv-s, (adv-s (without.p (a.d doubt.n)));

however, negation is transparent in the usual sense – the truth value of a negated sentence depends only of the truth value of the unnegated sentence.

Modifiers of sort .adv-e are transparent, typically implying temporal or locative constraints, e.g.,

today.adv-e, (adv-e (during.p (the.d drought.n))), (adv-e (in.p |Rome|));

these constraints are ultimately cashed out as predications about episodes characterized by the sentence being modified. (This is also true for the past and pres tense operators.)

Similarly any modifier of sort .adv-f is transparent and implies the existence of a multi-episode (characterized by the sentence as a whole) whose temporally disjoint parts each have the same characterization (Hwang & Schubert, 1994); e.g.,

regularly.adv-f, (adv-f ({at}.p (three.d (plur time.n)))).

The relative scoping of these operators are left ambiguous at the ULF stage, just as with quantifiers and tense. (Kim & Schubert, 2017) introduced this approach to sentence modification annotation and provides further details and examples. They also discuss methods to handle tense and aspect annotation, which are closely related to sentence modification. We adopt their approach in our work.

Flat Bracketing & Localized Modification

In describing predicate and sentence modification, we’ve loosely described the relaxations for operator positioning. Here we discuss the subtleties in operator positioning, motivate the relaxations, and specify the exact constraints.

We refine and generalize the operator-lifting technique of sentence-level operators described by (Kim & Schubert, 2017) to verb phrases in order to eliminate word reordering when annotating sentences like “Mary undoubtedly spoke up”. To summarize the approach from (Kim & Schubert, 2017), sentence-level operators (e.g. .adv-e, .adv-s, etc.) located in the middle of the sentence, e.g. (|Mary| (undoubtedly.adv-s (past speak_up.v))), can be automatically lifted to sentence-level since the semantic type makes its necessary position clear. The example just given would lift undoubtedly.adv-s to sentence level resulting in the formula (undoubtedly.adv-s (|Mary| (past speak_up.v))). (The same would be done for past when fully processing the sentence).

There are a few refinements need to be made for the approach described by (Kim & Schubert, 2017).

We need to add restrictions of lifting the operators to the nearest distinct predications such as within embedded sentences and type-shifters.
We need to introduce a mechanism for sentence-level operators scoped over non-sentence contexts.
A similar lifting operation is necessary for verb modifiers that can occur in constituent, rather than premodifying position.

I’ll discuss these in order.

Notice that in the following sentences

(1) I know that he didn’t go home,
(2) I saw the boy that didn’t take the ice cream, and
(3) I like to not stay up late

the negations are all restricted to their respective clauses and shouldn’t be lifted to modify the top-level sentence. That is, (1) is equivalent to saying I know that it is not the case that he went home. If we were to lift the negation all the way to the top we get a meaning that we definitely don’t want: *It is not the case that I know that he went home. (1) and (2) are cases where the negation is restricted to an embedded sentence. (3) however restricts it to a verb phrase. This seems to happen due to the reification of the verb phrase via the ka operator. Notice this holds for I like to bake cakes regularly. The liking is happening regularly, it’s the baking that is regular. Therefore, during the lifting phase, the lifting will only happen to the nearest sentence or type-shifter. Here we list the raw ULF interpretations for each of the sentences just discussed and the transformed versions after lifting. You may notice that there is still some discrepancy in the annotation of sentence-level operators against (Kim & Schubert, 2017). This will be cleared up in the discussion of the other refinedments.

(1) I know that he didn’t go home
raw ULF

(i.pro ((pres know.v) 
        (that (he.pro ((past do.aux-s) not 
                       (go.v (adv-a ({to}.p (k home.n)))))))))

post-lifted ULF

(i.pro ((pres know.v) 
        (that (not (he.pro ((past do.aux-s) 
                            (go.v (adv-a ({to}.p (k home.n))))))))))

(2) I saw the boy that didn’t take the ice cream
raw ULF

(i.pro ((past see.v) 
        (the.d (n+preds boy.n 
                        (that.rel ((past do.aux-s) not 
                                   (take.v (the.d (ice.n cream.n)))))))))

post-lifted ULF

(i.pro ((past see.v) 
        (the.d (n+preds boy.n 
                        (not (that.rel ((past do.aux-s) 
                                        (take.v (the.d (ice.n cream.n))))))))))

(3) I like to not stay up late
raw ULF

(i.pro ((pres like.v) (to (not (stay_up.v late.adv-e)))))

post-lifted ULF

(i.pro ((pres like.v) (to (not (late.adv-e stay_up.v)))))

(4) I like to bake cakes regularly
raw ULF

(i.pro ((pres like.v) (to (bake.v (k (plur cake.n)) regularly.adv-f))))

post-lifted ULF

(i.pro ((pres like.v) (to (regularly.adv-f (bake.v (k (plur cake.n)))))))

The type compositions don’t work out for the kind-of-action restriction of the sentence-level operator, as in (to (regularly.adv-f (bake.v (k (plur cake.n))))) since regularly.adv-f is a sentence modifier (\((\mathcal{S} \rightarrow \mathcal{2}) \rightarrow (\mathcal{S} \rightarrow \mathcal{2})\)) whereas (bake.v (k (plur cake.n))) is a monadic verbal predicate (\(\mathcal{N}_{V}\) or \((\mathcal{D} \rightarrow \mathcal{S} \rightarrow \mathcal{2})_{V}\)). How this is handled will be clarified when we discuss the next refinement. We need to generate an appropriate lambda expression to capture this.

The sentence-level operator will be restricted by the following contexts:

Reification operators (e.g. examples (3) and (4))
The predicate-argument boundary (e.g. not in The railing helps me not fall over evaluates over fall over, not the whole verb phrase)
Type shifters (e.g. surprisingly in The surprisingly happy man walked in evaluates over the scope of happy, not the main verb)

What all this reduces to is that a sentence-level operator lifts up the most restrictive complete predication to act over. Reification results in a completely separate predication between the predication in the reification context and the predication resulting from the main verb of the sentence. Similarly, when a predicate is an argument of the main verb, the main verb causes some modification to or comments on the predication resulting from its argument, but the main verb overall makes a separate predication. Consider the example above, The railing helps me not fall over. help operates over me and not fall over, in that the subject of help assists me to realize the predicate not fall over, but the actual predication of help (described by the complete sentence) is distinct from the predication resulting from the argument: me not falling over. In a sense 1) is a special case of 2). We know that once we reify something, the predicate within can’t be forming the main verb, so the reified result must be used as an argument somewhere.

Refinement 2: Mechanism for sentence-level operators scoped over non-sentence contexts

The lifting restrictions from refinement 1 leads to the problem that sentence level operators now scope over non-sentence objects, e.g. (ka (not fall_over.v)). This is problematic to the idea of composition through semantic types which ULF holds at its core. We assume an implicit expansion to the necessary type with additional unspecified constituents. Within ULF these constituents are fully unspecified, but would be fully resolved upon deindexing the specific predication. Then an implicit lambda expression wraps around the sentence-level operator with these unspecified arguments as the variables. This preserves the type of the predicate. For example, (ka (not (fall_over.v))) has the implicit lambda expression (ka (lambda x (not (x fall_over.v)))). Below are a few examples of this.

(3) I like to not stay up late
post-lifted ULF

(i.pro ((pres like.v) (to (not (late.adv-e stay_up.v)))))

showing implicit lambdas

(i.pro ((pres like.v) (to (lambda x (not (late.adv-e (x stay_up.v)))))))

(4) I like to bake cakes regularly
post-lifted ULF

(i.pro ((pres like.v) (to (regularly.adv-f (bake.v (k (plur cake.n)))))))

showing implicit lambda

(i.pro ((pres like.v) 
        (to (lambda x (regularly.adv-f (x (bake.v (k (plur cake.n)))))))))

(5) The railing helps me not fall over
post-lifted ULF

((the.d railing.n) ((pres help.v) me.pro (not fall_over.v)))

showing implicit lambdas

((the.d railing.n) ((pres help.v) me.pro (lambda x (not (x fall_over.v)))))

(6) The surprisingly happy man walked in
post-lifted ULF

((the.d ((surprisingly.adv-s happy.a) man.n)) ((past walk.v) in.adv-a))

showing implicit lambdas

((the.d ((lambda x (surprisingly.adv-s (x happy.a))) 
         man.n)) 
 ((past walk.v) in.adv-a))

Although at first we expected to be able to handle verb modifier placement by simply allowing arbitrary order, this isn’t sufficient for ditransitive verbs since the modifier can be interleaved between the arguments, e.g. Sally gave a book quickly to John. Therefore, what we’ve settled on is that all non-subject arguments and modifiers of a verb are supplied as constituents at the same level. The modifiers can then be lifted to the expected prefix position in post-processing and arguments are supplied to the verb in the provided order. Consider the annotation of the following sentence.

(7)Alice delivered the artifact carefully to the curator today

(|Alice| ((past deliver.v) (the.d artifact.n)
                           carefully.adv-a
                           (to.p-arg (the.d curator.n))
                           today.adv-e))

Notice that we can combine the relaxed context of verbal and sentence modifiers. This flat form of supplying arguments and modifiers allows us to mostly preserve word order and simplify the bracketing structures. After lifting the modifiers, carefully.adv-a and today.adv-e, we get

(today.adv-e (|Alice| (carefully.adv-a 
                       ((past deliver.v) (the.d artifact.n)
                                         (to.p-arg (the.d curator.n))))))                 

Here is the same thing for the other example given above

(8) Sally gave a book quickly to John

(|Sally| ((past give.v) (a.d book.n)
                        quickly.adv-a
                        (to.p-arg |John|)))

After lifting

(|Sally| (quickly.adv-a ((past give.v) (a.d book.n) 
                                       (to.p-arg |John|))))

Just as with sentence-level operators, these verb modifiers can also be supplied in a manner that doesn’t require lifting. That is, scoped over the whole verb phrase. For example,

(9) Jenn quickly wrote the report

(|Jenn| (quickly.adv-a ((past write.v) (the.d report.n))))

(10) Jim declined the request politely

(|Jim| (((past decline.v) (the.d request.n)) politely.adv-a))

For the motivating examples (7) and (8), this would require changing the word order. Since the verb modifiers are interleaved with the direct objects and indirect objects, they cannot scope around the full verb phrase in the given positions. For reference, the flattened versions of those ULFs would be

(9’) (|Jenn| (quickly.adv-a (past write.v) (the.d report.n)))

(10’) (|Jim| ((past decline.v) (the.d request.n) politely.adv-a))

Note that the order of constituents in these flattened phrases are important. Although the modifiers are lifted out of the given position and moved to the verb phrase, the first verb when scanned left to right is considered the acting verb and the following arguments are interpreted in the English word order. So for example, (quickly.adv-a (the.d report.n) (past write.v)) is not valid since after lifting we get (quickly.adv-a ((the.d report.n) (past write.v))) which looks like we’re trying to apply a verb modifier to a sentence. (Left supplied verb arguments are assumed to be the subject).

Summary

Intensional predicate modification is done through functions from monadic predicates to monadic predicates, \(\mathcal{N} \rightarrow \mathcal{N}\), which have suffix types .mod-a, .mod-n, and .adv-a for adjective, noun, and VP modification, respectively.
Predicate modifiers can be formed via type-shifters from monadic predicates (mod-a, mod-n, adv-a) or individuals (nnp).
mod-a and mod-n type-shifters can be omitted if their first argument is not a verb and the resulting modifier is premodifying the other noun (e.g. (happy.a dog.n) omits mod-n, but ((mod-n (carefully.adv-a (pasv write.v))) notice.n) cannot omit the mod-n).
When the types are explicit in ULF, the operator position can be either prefixed or infixed.
Intersective modification such as noun post-modification is handled through macros that map to equivalent lambda expressions.
Sentence-level operators are lifted to the nearest predication.
Verb modifiers can be interleaved with non-subject arguments and automatically lift to prefix position.

ULF Intro 3 - Inference with ULFs

2019-01-07T19:00:00-08:00

An important insight of NLog research is that language can be used directly for inference, requiring only phrase structure analysis and upward/downward entailment marking (polarity) of phrasal contexts. This means that NLog inferences are situated inferences, i.e. their meaning is just as dependent on the utterance setting and discourse state as the linguistic “input” that drives them. This insight carries over to ULFs, and provides a separate justification for computing ULFs, apart from their utility in the process of deriving deep, context-independent, canonicalized meaning representations from language.

ULFs in principle provide a more reliable and more general basis for situated inference than phrase structure, because of the coherent semantic type structure they encode. Greater reliability also leads to the possibility of spontaneous forward inferencing, as opposed to inference guided by systems classifying already provided hypotheses as entailments, contradictions, or neutral in relation to some reference sentence (as in most textual entailment and NLog studies to date – e.g. SNLI, MNLI). Forward inference is important because human language understanding seems to involve continuous forward inferencing. Imagine reading the following sentence in a paper or newsfeed

Police reported that the vehicle struck several cars

you will conclude that

(a) the reported event almost certainly happened,

and further,

(b) that the cars involved were all damaged.

Conclusion (a) requires only a small amount of knowledge about communication, to the effect that reporting (in your preferred media) typically involves reporting of facts; whereas conclusion (b) depends on very specific world knowledge. We expect to show ULF utility for forward inference in cases like conclusion (a), since accumulation of sufficient world knowledge for enabling such inferences seems practical. In principle, ULF could support inferences resulting in conclusion (b) – within the bounds of ULF ambiguity – but the necessary world knowledge remains out of reach in the short run. As a whole it’s unreasonable to expect that an inference system will have a set of alternative hypotheses to choose from. Rather, the system needs to be able to generate inferences directly.

The rules for generating inference (a) could be as simple as

(all_wfulf w
  ((something.pro ((past report.v) (that w)))
   => ((the.d (event-of w)) probably.adv-s (past happen.v))))

where all_wfulf denotes substitutional quantification over well-formed ULF formulas. Substitutational quantification quantifies over substitutions of expressions of a particular category of metavariable. (Morbini & Schubert, 2008) describes the details of this mechanism and how it fits into object level semantics. We can take the ULF formula for the report above

;; "Police reported that the vehicle struck several cars"
((k police.n)
 ((past report.v)
  (that ((the.d vehicle.n) ((past strike.v) (several.d (plur car.n)))))))

and conclude

;; "The event of 'the vehicle struck several cars' probably happened"
((the.d (event-of ((the.d vehicle.n) ((past strike.v) (several.d (plur car.n))))))
 probably.adv-s (past happen.v))

We ended up relying on a non-standard operator event-of here for simplicity. This could be translated into using the characterizing operator **, which is implicit in strict ULF.

Propositions vs Events

To get more concrete about the role of the semantic types in generating inferences, consider the distinction between propositions and events. Propositions are abstract, true or false information objects and as such can be asserted, known, believed, disputed, etc.; whereas events are surely real, temporal entities in the world, often with causal consequences – without them, there would be no natural or social world as we know it. Here are two sentences that demonstrate this distinction,

(1) Molly barked last night; that woke up the neighbors.

(2) Molly barked last night; that’s what the neighbors assert.

Note that propositions don’t wake neighbors, but events certainly can; and events can’t be asserted, but propositions certainly can. As such that in the two sentences must refer to distinct entities (that in (1) refers to an event and that in (2) refers to proposition). Events can have temporal parts at any scale, and can physically involve many entities, but propositions cannot. Propositions and events are easily confused because they are closely related: natural language sentences express propositions and at the same time characterize events or situations. But an adequate semantic representation must distinguish them, thus providing distinct referents for the two instances of the anaphoric that in the above sentences. For a full discussion see (Schubert & Hwang, 2000) and also (Zucchi, 1989). In general, propositions believed (or rejected) by people are central to explaining the reasons for their actions, while events interact causally. In EL, the propositional referent in the second sentence is provided simply by applying the sentence reifying operator, that to the meaning of the sentence, whereas the event is generated during the deindexing process. Basing inferences on sharp distinctions of propositions and episodes as described is justified in detail in (Schubert & Hwang, 2000).

Of course the other semantic types: various subcategories of predicates, kinds of actions, kinds of events, general kinds, numbers, collections, predicate modifiers, etc. also make distinctions important to inference. The most crucial aspect of ULF in supporting justified inferences, however, is the coherent semantic composition. So long as antecedents of inference rules operate over fragments of well-formed ULF and consequents respect the semantic types during any restructuring, we can be certain that conclusions will have coherent semantic structures.

Here are some kinds of inferences we can expect ULFs to support:

NLog inferences based on generalizations/specializations

The sentence “Every NATO member sent troops to Afghanistan”, together with the knowledge that France is a NATO member and that Afghanistan is a country entails that France sent troops to Afghanistan and that France sent troops to a country.

((every.d (member-of.n |NATO|))
 ((past send.v) (k (plur troop.n))
                (to.p-arg |Afghanistan|)))

We won’t get into the details of computing contextual polarity here, but simply state that NATO member is in positive context and Afghanistan is in negative context. Positive context allow specializations, whereas negative contexts allow generalization of the predicates while retaining truth conditions. So we can resolve the right side of (|France| ((pres be.v) (member-of.n |NATO|))) into the sentence to get

((every.d (= |France|))
 ((past send.v) (k (plur troop.n))
                (to.p-arg |Afghanistan|)))

then resolve the left hand side of (|Afghanistan| ((pres be.v) (= (a.d country.n)))) to get

((every.d (= |France|))
 ((past send.v) (k (plur troop.n))
                (to.p-arg (a.d country.n))))

Right now we get the awkward, but not incorrect sentence of Everything that is France sent troops to a country. We can simplify to just France sent troops to a country with an intuitive inference rule (all x (every.d (= x)) x). Simply put, if we’re quantifying over everything that is logically equal to a particular entity, it’s just going to be that entity. We can use it to clean up the formula.

(|France| ((past send.v) (k (plur troop.n)) (to.p-arg (a.d country.n))))

Such inferences are within the scope of NLog-based and ULF-based methods, and can help in finding inference paths to candidate entailments; but they will not be our focus as they rarely seem worthwhile as spontaneous forward inferences from sentences in discourse (we are particularly interested in dialogue settings).

NLog inferences based on implicatives

“She managed to quit smoking” entails that She quit smoking (and the negation of the premise leads to the opposite conclusion). We already demonstrated such inferences using fully-resolved Episodic Logic for various headlines (Stratos et al., 2011), such as the inference from Oprah is shocked that Obama gets no respect (Fox News 2011) to Obama gets no respect. Such inferences are surely important – and immediate – in language understanding. Here is a simplified walk through of generating these inference in ULF to give an idea of how this is handled.

We have the formula

(F1) (she.pro ((past manage.v) (to (quit.v (ka smoke.v)))))

and an inference rule for manage, which we’ll call (R1)

(all_ulfvp w
  (all x
    ((x ((past manage.v) (to w)))
     => (past (x w)))))

We can resolve the term she.pro in (F1) to x in (R1) and the ULF VP predicate (quit.v (ka smoke.v)) in (F1) to w in (R1). When we run (R1) with this resolution, we conclude

(past (she.pro (quit.v (ka smoke.v))))

This gives us the meaning we’re looking for of She quit smoking. The past is placed at the sentence level for simplicity (and it’s not incorrect since past is actually a sentence level operator anyway), but the tense can also be automatically inserted into the VP where it would normally appear in ULF using a more complicated pattern matching procedure in the inference rule.

Inferences based on attitudinal and communicative verbs

This category of inferences intersects a bit with inferences from implicatives that we just described. For example, we can conclude from both of the sentences

We know that coffee is a fruit

They found out that coffee is a fruit

that the proposition coffee is a fruit is true in a way that is very similar to what was shown for “manage” in the previous section. However, attitudinal and communicative verbs can also involve probabilistic reasoning, structural elaboration, and depend of constituent types – all of which would be difficult to capture within NLog. Consider the sentence

John denounced Bill as a charlatan

(F2)

(|John| ((past denounce.v)
         |Bill|
         (as.p-arg (= (a.d charlatan.n)))))

We can conclude from this sentence that (a) John probably believes that Bill is a charlatan, (b) John asserted to his listeners (or readers) that Bill is a charlatan, and (c) John wanted his listeners (or readers) to believe that Bill is a charlatan. Notice that these inferences go beyond just relating embedded events and propositions with truth values, but relate the arguments in more complex ways.

Inference (a) could be captured with a simple lexical inference rule like the following

(R2)

(all_ulfpred w
  (all x (all y
    ((x ((past denounce.v) y (as.p-arg w)))
     => (x probably.adv-s ((pres believe.v) (that (y ((pres be.v) w)))))))))

By resolving |John|, |Bill| and (= (a.d charlatan.n)) in (F2) to x, y, and w in (R2), respectively, we conclude the formula for

John probably believes that Bill is a charlatan

(|John| probably.adv-s
 ((pres believe.v)
  (that (|Bill| ((pres be.v) (= (a.d charlatan.n)))))))

With some additional complexity, this could be generalized to other communicative verbs that use the [verb]-[direct object]-[p-arg] construction (e.g. declare).

Inference (b) and (c) can be captured with a rules which can be generalized to just about any communicative verb.

(R3)

(all_ulfpred w
  (all x (all y
    ((x ((past denounce.v) y (as.p-arg w)))
     => (x ((past assert.v)
            (adv-a (to.p ((x 's) ((plur reader.n) or.cc (plur listener.n)))))
            (that (y ((pres be.v) w)))))))))

(R4)

(all_ulfpred w
  (all x (all y
    ((x ((past denounce.v) y (as.p-arg w)))
     => (x ((past want.v)
            ((x 's) ((plur reader.n) or.cc (plur listener.n)))
            (to (believe.v (that (y ((pres be.v) w)))))))))))

By again resolving |John|, |Bill|, and (= (a.d charlatan.n)) to x, y, and w, respectively in each of (R3) and (R4), we conclude inferences (b) and (c).

John asserted to his readers or listeners that Bill is a charlatan

(|John| ((past assert.v)
         (adv-a (to.p ((|John| 's) ((plur reader.n) or.cc (plur listener.n)))))
         (that (|Bill| ((pres be.v) (= (a.d charlatan.n)))))))

John wanted his readers or listeners that Bill is a charlatan

(|John| ((past want.v)
         ((|John| 's) ((plur reader.n) or.cc (plur listener.n)))
         (to (believe.v (that (|Bill| ((pres be.v) (= (a.d charlatan.n)))))))))

(R3) and (R4) could be generalized so that denounce.v is replaced by any other communicative verb that occurs in this argument context. Or by generalizing past to the different tenses.

(R2) gives us a good opportunity to highlight the importance of the types in generating inferences. Given a sentence like “Mary denounced Bill as well”, we wouldn’t want to infer that Mary believes that Bill is well. Here’s the ULF annotation of this sentence.

(|Mary| ((past denounce.v) |Bill| as_well.adv-s))

Since “as well” in this sentence is an adverbial, not an argument, the antecedent of (R2) won’t be able to unify with this sentence.

Inferences based on counterfactuals

“If I were rich, I would pay off your debt” and “I wish I were rich” both implicate that the speaker is not rich. This depends on recognition of the counterfactual form, which is distinguished in ULF. Consider, for example, the ULF for the first sentence.

(F3)

((if.ps (i.pro ((cf were.v) rich.a)))
 (i.pro ((cf will.aux-s) pay_off.v (your.d debt.n))))

cf is the counterfactual marker that sits in the same position as the tense marker in the sentence. We can then write inferences over sentences like this by identifying the counterfactual marker and asserting the negation of the sentence it operates over. These inference rules must interact with ULF syntax analysis so we will use predicates over ULF syntax, embedded-within? and functions over the syntax, tense-of! and with-tense!.

(R5)

(all_wfulf w1
  (all_wfulf w2
    (((embedded-within? w1 w2) and.cc ((tense-of! w1) = cf))
     => (not (with-tense! w1 pres)))))

embedded-within? returns true if the first argument is embedded within the second argument. For example, (i.pro ((cf were.v) rich.a)) in the formula (F3). tense-of! returns the tense of the given ULF formula. with-tense! returns the ULF formula of the first argument modified to have the tense given in the second argument.

We can unify (F3) to w2 in (R5) and (i.pro ((cf were.v) rich.a)) to w1 in (F3) to run the inference rule. We just described why (embedded-within? w1 w2) is true, and clearly (tense-of! w1) will be cf. If we replace the tense in w1 with pres and negate it as described in (R5), we conclude

(not (i.pro ((pres were.v) rich.a)))

We can either add some post-processing or add some complexity to the (R5) to deal with the fact that were.v is only possible in counterfactual form and should be mapped to be.v.

Inferences from questions and requests

“When are you getting married?” enables the inference that the addressee will get married (in the foreseeable future), and that the questioner wants to know the expected date of the event, and expects that the addressee probably knows the answer, and will supply it. Similarly an apparent request such as “Could you close the door?” implies that the speaker wants the addressee to close the door, and expects he or she will do so. There are subtleties in the distinction between questions and requests that can be captured in ULF and made use of.

We’ll walk through a simple example with “Who did you see yesterday?”. From this we infer the presupposed knowledge that you did meet someone yesterday. Let’s start with the ULF of the sentence.

(F4)

((sub who.pro ((past do.aux-s) you.pro (see.v *h yesterday.adv-e))) ?)

All the wh-phrases in English can be modified to make a statement with using “some”. who corresponds to someone, where corresponds to somewhere, why correpsonds to for some reason, etc. So again, we assume the existence of a predicate wh-sent? and functions wh-sent-to-some-sent! and uninvert-sent! over the ULF syntax.

(R6)

(all_wfulf w
  (((w ?) and (wh-sent? w))
   => (uninvert-sent! (wh-sent-to-some-sent w))))

The predicate and function over the syntax of ULF is used because wh-words can occur in many places in the sentence. This means a syntactic analysis rather than a case-by-case inference system is better suited for this problem.

Running (R6) over (F4) gives us

(sub someone.pro (you.pro ((past do.aux-s) (see.v *h yesterday.adv-e))))

in English, “Someone you did see yesterday”. We can get a more natural reading by applying the sub macro and running an inference rule for eliminating the do.aux-s, which is an auxiliary almost solely used for question inversions with minimal semantic influence.

(you.pro ((past see.v) someone.pro yesterday.adv-e))

in English, “You saw someone yesterday”.

Prev: ULF Intro 2

ULF Intro 2 - Role of ULF in Comprehensive Semantic Interpretation

2019-01-07T18:00:00-08:00

ULFs are underspecified – loosely structured and ambiguous – in several ways. But their surface-like form, and the type structure they encode, make them well-suited to reducing underspecification, both using well-established linguistic principles and machine learning techniques that exploit the distributional properties of language. The image below shows a diagram of the interpretation process from an English sentence to full-fledged Episodic Logic and highlights where ULF fits into it. The structural dependencies in the diagram are shown with solid black arrows and information flow is shown with dashed blue arrows. The backwards arrows exist because the optimal choice at a particular step depends on the overall coherence of the final formula and such coherence information can be used to make decisions in structurally preceding steps. Word sense disambiguation and anaphoric resolution don’t interact with the general structure of the formula so they can be incorporated at any point in the process. The yellow highlighting shows the components of the formula that changed from the previous structurally dependent step in the process.

Let’s walk through this diagram. We start of with the sentence

She wants to eat the cake

which is interpreted into the following ULf

(she.pro ((pres want.v) (to (eat.v (the.d cake.n)))))

After tense and determiner scoping (lifting up pres and the.d) it becomes

(pres (the.d (x cake.n) (she.pro (want.v (to (eat.v x))))))

This is then deindexed, Skolemized, and canonicalized (if you don’t understand these terms, read the subsections below) to

(|E|.sk at-about.p |Now17|),
((the.d x (x cake.n) (she.pro (want.v (to (eat.v (the.d cake.n)))))) ** |E|.sk)

|E|.sk is a Skolemized episode variable, which is characterized by the sentence via the ** operator. Once we’ve resolved who she is and what the cake is, we can appropriately substitute for them. Say this is the third cake introduced to the domain of discourse and we know that she is referring to “Chell”. Then we resolve those conclusions to get

(|E|.sk at-about.p |Now17|),
((|Chell| (want.v (to (eat.v |Cake3|)))) ** |E|.sk)

We can wrap up by performing word sense disambiguation on all the predicates to get

(|E|.sk at-about.p |Now17|),
((|Chell| (want1.v (to (eat1.v |Cake3|)))) ** |E|.sk)

We have developed and applied heuristic algorithms that resolve scope ambiguities and make event structure explicit. Though these algorithms are not sufficiently reliable, they set a baseline for future work. We now discuss each of these resolutions steps in more detail and how ULF supports these later resolutions steps.

Word sense disambiguation (WSD)

Is “bass” a fish or instrument?

(1) I went fishing for some sea bass

(2) The bass line is too weak

One obvious form of underspecification is word sense ambiguity. But while, for example, (weak.a (plur creature.n)) does not specify which of the dozen WordNet senses of weak or three senses of creature is intended here, the type structure is perfectly clear: A predicate modifier is being applied to a nominal predicate. Certainly standard statistical WSD techniques (Jurafsky & Martin, 2009) can be applied to ULFs, but this should not in general be done for isolated sentences, since word senses tend to be used consistently over longer passages. It should be noted that adjectives appearing in predicative position (e.g., able in able to succeed – (be.v (able.a (to succeed.v))) or in attributive position (e.g., little in three little bushes – (three.d (little.a (plur bush.n))) are type-distinct in EL, but ULF leaves this distinction to further processing, since the semantic type of an adjective is unambiguous from the way it appears in ULF.

Predicate adicity

How many arguments does a predicate take?

A slightly subtler issue is the adicity of predicates. We do not assume unique adicity of word-derived predicates such as run.v, since such predicates can have intransitive, simple transitive and other variants (e.g., run quickly vs. run an experiment). But adicity of a predicate in ULF is always clear from the syntactic context in which it has been placed – we know that it has all its arguments in place, forming a truth-valued formula, when an argument (the “subject”) is placed on its left, as in English. It is for this reason that arguments that are implicit in the surface sentence are introduced in ULFs, such as in example 1 from ULF Intro 1,

Could you dial for me?

(((pres could.aux-v) you.pro (dial.v {ref1}.pro
                                     (adv-a (for.p me.pro)))) ?)

In this example, {ref1}.pro is not in the surface sentence, but a known necessary argument of dial for this sentence to make sense.

Scope ambiguity

Every dog sees a bone

Does every dog see the same bone?

The sentence above has two possible relative scopings of the two determiners, every and a, which give distinct readings of the sentence. Either, there can be a bone with respect to each of every dog as in the following

(every.d x: (x dog.n) (a.d y: (y bone.n) (x ((pres see.v) y))))

or there could be a bone that is seen by every dog which would be resolved as below.

(a.d y: (y bone.n) (every.d x: (x dog.n) (x ((pres see.v) y))))

This sort of ambiguity can arise from the three types of unscoped elements in ULF, which are determiner phrases derived from noun phrases (such as very few people and the Earth – ((nquan (very.mod-a few.a)) (plur person.n) and (the.d |Earth|.n), respectively), the tense operators pres and past, and the coordinators and.cc, or.cc and some variants of these. The positions they can “float” to in postprocessing are always pre-sentential, and determiner phrases leave behind a variable (e.g. x and y in the motivating example about the dog and the bone above) that is then bound at the sentential level. This view of scope ambiguity was first developed in (Schubert & Pelletier, 1982) and subsequently elaborated in (Hurum & Schubert, 1986) and reiterated in various publications by Hwang and Schubert.

The accessible positions are constrained by certain restrictions well-known in linguistics. For example, in the sentence

“Browder … claims that every oligarch in Russia was forced to give Putin half of his wealth”,

there is no wide-scope reading of every, to the effect “For every oligarch in Russia, Browder claims … etc.”; the subordinate clause is a “scope island” for strong quantifiers like every (as well as for tense). The ULF allows exploitation of such structural constraints, since it still reflects the surface syntax. Firm linguistic constraints still leave open multiple scoping possibilities, and many factors influence preferred choices, with surface form (e.g., surface ordering) playing a prominent role (Manshadi et al., 2013). So again the proximity of ULF to surface syntax will be helpful in applying ML techniques to determining preferred scopings.

Anaphora

John saw Bob and told him he had to go home

Who are “him” and “he”?

Another important aspect of disambiguation is coreference resolution. Again there are important linguistic constraints (“binding constraints”) in this task. For example, in “John said that he was robbed”, he can refer to John; but this is not possible in “He said that John was robbed”, because in the latter, he C-commands John, i.e., in the phrase structure of the sentence, it is a sibling of an ancestor of John. ULF preserves this structure, allowing use of such constraints. In the ULF for these sentences,

(|John| ((past say.v) (that (he.pro (past (pasv rob.v))))))

(he.pro ((past say.v) (that (|John| (past (pasv rob.v))))))

we see that in the former formula, |John| is the sibling of the verb phrase ((past say.v) (that (he.pro (past (pasv rob.v))))), which indeed is an ancestor of he.pro. Similarly, in the latter formula, we get the opposite since he.pro and |John| are in opposite positions.

Preservation of structure also allows application of ML techniques (Poesio et al., 2016), but again this should be done over passages, not individual sentences, since coreference “chains” can span many sentences. When coreference relations have been established as far as possible and operators have been scoped, the resulting LFs are quite close in form to first-order logic, except for incorporating the additional expressive devices (generalized quantifiers, modification, attitudes, etc.) that we have already mentioned and illustrated. In our writings we call this the indexical logical form, or ILF. ILF doesn’t appear in the intepretation process diagram due to the particular decomposition of steps we show in the diagram. The anaphora resolution is shown as a structurally independent step from the core structural changes. However, it is required for the final EL interpretation.

Event/situation structure

What are the events in the sentence and how do they relate?

The critical aspect of episodic logical form is event/situation structure. Much of the past work in EL has been concerned with the principles of de-indexing, i.e., making events and situations – episodes in our terminology – explicit (Hwang, 1992; Hwang & Schubert, 1994; Schubert, 2000). The relationship to Davidsonian event semantics and Reichenbachian tense-aspect theory is explained in these references. Their compositional approach to tense-aspect processing leads to construction of a so-called tense tree, and yields multiple, related reference events for sentences such as “By 8pm tonight, all the employees will have been working for 15 hours straight”. The compositional constuction and use of tense-trees is possible only if the logical form being processed reflects the original clausal structure – as ULF indeed does. This step is merged with the following, canonicalization step in the diagram above.

The EL approach to the semantics of tense, aspect, and temporal adverbials differs from the traditional Davidsonian approach in that it associates episodes not only with atomic predications, but also with negated, quantified, and other complex sentences. For example, in ELF there is an explicit referent available for the phrase this situation in sentence pairs such as “No rain fell for two months. *This situation* led to crop failures”, or “Every theater patron was trying to exit through the same door. *This situation* led to disaster”. In addition, we regard perfect and progressive aspect, via operators perf and prog, together with the tense operators pres and past and modal auxiliary will.aux-s, as contributing to temporal structure compositionally, rather than by enumeration of possible tense-aspect combinations. The compositional process is mediated by tense trees systematically determined by ULF structure. The process deposits, and makes reference to, episode tokens at tense tree nodes, relating the various times/episodes referred to in sentences such as By 8pm tonight, all the employees will have been working for 15 hours straight”. Details are provided in the publications above, especially (Hwang & Schubert, 1994).

Canonicalization

Finally, canonicalization of ELF into “minimal” propositions, with top-level Skolemization (and occasionally \(\lambda\)-conversions), is straightforward. Some complex examples are shown in prior publications (Schubert & Hwang, 2000; Schubert, 2014; Schubert, 2016).

When episodes have been made explicit (and optionally, canonicalized), the result is episodic logical form (ELF); i.e., we have sentences of Episodic Logic, as described in our previously cited publications. These can be employed in our Epilog inference engine for reasoning that combines linguistic semantic content with world knowledge. A variety of complex Epilog inferences are reported in (Schubert, 2013), and (Morbini & Schubert, 2011) contained examples of self-aware metareasoning. Further in the past, Epilog reasoned about snippets from the Little Red Riding Hood story: If the wolf tries to eat LRRH when there are woodcutters nearby, what is likely to happen?”; answer chain: The wolf would attack and try to subdue LRRH; this would be noisy; the woodcutters would notice, and see that a child is being attacked; that is a wicked act, and they would rush to help her, and punish or kill the wolf (Hwang, 1992; Schubert & Hwang, 2000). However, the scale of such world-knowledge-dependent reasoning has been limited by the difficulty of acquiring large amounts of inference-enabling knowledge. (The largest experiments, showing the competitiveness of Epilog against state-of-the art theorem provers were limited to formulas of first-order logic (Morbini & Schubert, 2009).) In the proposed work we therefore focus on inferences that are important but not heavily dependent on world knowledge.

The potential of EL reasoning has been extensively demonstrated, making the prospect of effectively mapping language to EL an attractive one. The most complete [language \(\rightarrow\) reasoning] system built so far (2012-14) was a system for interpreting captions of family photos (e.g., Alice, with her two grandmothers at her graduation party), then aligning the caption-derived knowledge with image-derived data about individuals’ apparent age, gender, hair color, eye-wear, etc., merging the knowledge, and then inferentially answering questions (Who graduated?). Unpublished reports (to ONR) on this work exist, but further development has been hampered by difficulties in obtaining large collections of captioned family photos for scaling up.

Thus ULFs comprise a “primal” logical form whose resemblance to phrase structure and whose constraints on semantic types provide a basis for the multi-faceted requirements of deriving less ambiguous, nonindexical, canonical LFs suitable for reasoning. However, as we have pointed out, ULFs are themselves inference-enabling, and this will be important for our evaluation plan.

Prev: ULF Intro 1

Next: ULF Intro 3

ULF Intro 1 - Introduction to ULF Type Structure

2019-01-07T17:00:00-08:00

The following six examples provide an idea of the language-like syntax of ULFs. The first two are from the Tatoeba database, the next three are from The Little Prince (which was used for the first AMR-annotated corpus), and the last is from the Web:

Could you dial for me?

(((pres could.aux-v) you.pro (dial.v {ref1}.pro 
                           (adv-a (for.p me.pro)))) ?)

If I were you I would be able to succeed.

((if.ps (I.pro ((cf were.v) (= you.pro))))
 (I.pro ((cf will.aux-s) 
      (be.v (able.a (to succeed.v)))))) 

He neglected three little bushes

(he.pro ((past neglect.v) 
      (three.d (little.a (plur bush.n)))))

Flowers are weak creatures

((k (plur flower.n)) ((pres be.v) 
                   (weak.a (plur creature.n))))

My drawing is not a picture of a hat

((my.d drawing.n) ((pres be.v) not
                (= (a.d (picture-of.n (a.d hat.n))))))

Very few people still debate the fact that the earth is heating up

(((fquan (very.mod-a few.a)) (plur person.n)) still.adv-s 
  (debate.v (the.d (n+preds fact.n 
                         (= (that ((the.d |Earth|.n) 
                                   ((pres prog) heat_up.v)))))))))

As can be seen, ULF structure quite closely reflects phrase structure; and the type tags of atomic constituents, such as .pro, .v, .p, .a, .d, .n, etc., are intended to echo the part-of-speech origins of these constituents, such as pronoun, verb, preposition, adjective, determiner, noun, etc., respectively. Originally, ULFs contained some \(\lambda\)-abstracts, for example to form a conjunctive predicate from postmodified nouns, but we have introduced syntactic sugar elements that relieve annotators from coding such abstracts. An example is seen in (6): The n+preds macro takes a noun and one or more predicates as complements, and these are expanded into a \(\lambda\)-abstracted conjunctive predicate in postprocessing. As a result, ULFs are relatively amenable to human creation and intuitive interpretation. Moreover, as mentioned in the Introduction, the proximity to surface structure enables NLog-like inference and more.

But then isn’t parsing into ULF just another variant of syntactic parsing? The essential difference is that the type tags correspond to broad semantic categories (certain types of model-theoretic functions), and as such enable us to ensure that the type structure of ULFs – their operator-operand combinations – are semantically coherent. Richard Montague’s profoundly influential work can be viewed as demonstrating the crucial importance of paying attention to the semantic types of words and phrases, and that doing so leads to a view of language as very close to logic; as a result it lends itself to inference, at least to the extent that we can resolve – or are prepared to tolerate – various forms of ambiguity, context-dependence and indexicality.

Our semantic types are not as high-order as Montague’s, nor as “rigid” as Montague’s, but they suffice for maintaining type coherence. In particular, quantification is first-order, i.e., it iterates over individual entities, not over predicates, etc. – though through reification of predicate meanings and sentence meanings, we can “talk about” kinds of things, kinds of actions, propositions, etc., not just ordinary objects.

As soon as we take semantic types seriously in ULFs like the above, we see that certain type-shifting operators are needed to maintain type coherence. For example, in sentence (1) the phrase for me is coded as (adv-a (for.p me.pro)), rather than simply (for.p me.pro). That is because it is functioning here as a predicate modifier, semantically operating on the verbal predicate (dial.v {ref1}.pro) (dial a certain thing). Without the adv-a operator the prepositional phrase is just a 1-place predicate. Its use as a predicate is apparent in contexts like “This puppy is for me”. Note that semantically the 1-place predicate (for.p me.pro) is formed by applying the 2-place predicate for.p to the (individual-denoting) term me.pro. (Viewing \(n\)-place predicates as successively applied to their arguments, each time reducing the adicity, is in keeping with the traditions of Schönfinkel, Church, Curry, Montague, and others – hence “curried” predicates.) If we apply (for.p me.pro) to another argument, such as |Snoopy| (the name of a puppy), we obtain a truth value. So semantically, adv-a is a type-shifting operator of type (predicate \(\rightarrow\) (predicate \(\rightarrow\) predicate))), where the predicates are 1-place and thus of type (entity \(\rightarrow\) truth value). Of course, the name adv-a is intended to suggest “adverbial”, in recognition of the grammatical distinction between predicative and adverbial uses of prepositional phrases.

Then there is the issue of intensionality. For example, (2) is a counterfactual conditional, and the consequent clause “I would be able to succeed” is not evaluated in the actual world, but in a possible world where the (patently false) antecedent is imagined to be true. ULF and deeper LFs derived from it are based on a semantics where sentences are evaluated in possible situations (episodes), whose maxima are possible worlds. Details about syntactic forms and semantic types in the Episodic Logic approach to LF have been provided in many past publications (Hwang, 1992; Hwang & Schubert, 1994; Schubert & Hwang, 2000). This project website also contains separate posts that describe the syntax and semantic types in depth.

We don’t want to dive too deep for this introduction, but we note some further type-shifting operators in the examples to clarify the role of type-shifters in ULF. to (synonym: ka) in (2) shifts a verbal predicate to a kind (type) of action or attribute, which is an abstract individual; k in (4) shifts a nominal predicate to a kind of thing (so the subject here is the abstract kind, flowers, whose instances consist of sets of flowers; and that in (6) produces a reified proposition (again an abstract individual) from a sentence meaning. Through these type shifts, we are able to maintain a simple, classical view of predication, while allowing greater expressivity than the most widely employed logical forms, for example enabling generalized quantification (as in (6)), modification, reification, and other forms of intensionality.

The positioning of (adv-a (for.p me.pro)) within the verbal predicate it modifies, rather than in prefix-operator position, already indicates a certain looseness in the ULF syntax, as opposed to the rigidity of formal logic. This is unproblematic because we restrict the way operators may combine with operands so that type consistency is assured – and in fact in subsequent processing, any (adv-a (...)) constituents of a verbal predicate are moved so as to immediately precede that predicate. There are a number of further kinds of looseness in ULFs, but we defer further discussion to separate posts.

To wrap up this introductory discussion, we note a general concern that might be raised about ULFs. Since they largely conform with surface syntax, they are clearly language-specific. Isn’t the point of semantics to get at the deeper meanings underlying the surface forms or language, and shouldn’t these be somewhat uniform across languages? Our answer is two-fold: First, from a semantic perspective, the ULFs for different languages will have certain essential commonalities, namely, means to express predication, truth-functional and other connectives, generalized quantifiers, predicate and sentence modification, predicate and sentence reification, implicit and explicit reference to events/situations, comparatives, and a few other devices. Surface order is less important than these semantic commonalities. Second, we do think that sentence meanings should be factored into (as far as possible) minimal, separately usable, canonical propositions. This seems plausible both from speculations in cognitive science about “Mentalese”, and from a practical perspective, since canonicalization ensures that connections between ideas can be quickly recognized and used for inference. This canonicalization is the topic of the next post of the ULF introduction. Of course the meaning of sentences “in the wild” can be much more complex and subtle. Our hypothesis is that we can conquer those complexities effectively by starting with a type-coherent surface form, and systematically deriving canonical forms, bringing to bear many different kinds of influential factors. The next subsection elaborates on this view.

Next: ULF Intro 2

Unscoped (Episodic) Logical Forms

Some Thoughts on the Atemporal/Temporal Distinction

Atemporal Predicates in Natural Language?

Atemporal/temporal vs stage/individual

Modification in ULF

Prerequisite Knowledge

Predicate Modification

Actions, Experiences, and Attributes

Participial Phrases

Comparison of Modifier Notation Against Stanford Dependencies

Sentence Modification

Flat Bracketing & Localized Modification

Refinement 1: Restrictions of lifting the operators to the nearest distinct predication

Refinement 2: Mechanism for sentence-level operators scoped over non-sentence contexts

Refinement 3: Lifting functionality for verb modifiers

Summary

ULF Intro 3 - Inference with ULFs

Propositions vs Events

NLog inferences based on generalizations/specializations

NLog inferences based on implicatives

Inferences based on attitudinal and communicative verbs

Inferences based on counterfactuals

Inferences from questions and requests

ULF Intro 2 - Role of ULF in Comprehensive Semantic Interpretation

Word sense disambiguation (WSD)

Predicate adicity

Scope ambiguity

Anaphora

Event/situation structure

Canonicalization

ULF Intro 1 - Introduction to ULF Type Structure