## Welcome!

This is the ULF project page! This project is aimed at formulating, annotating, and parsing so-called unscoped logical forms (ULF) which is a representation for naturally capturing the semantic type structure of language within the framework of Episodic Logic (EL). ULF captures the predicate-argument structure in EL, staying faithful to the semantic types in EL theory, while leaving operator scopes, word sense, and anaphora for subsequent resolution. The underlying type system enables model-theory-supported structural inferences which are important for making conclusions driving forward in natural language interaction.

### ULF: A Primal Logical Form for Episodic Logic

Aspects of meaning unrelated to the semantic type structure are largely left ambiguous in ULFs for resolution in later steps. The purpose of this is to have a semantic representation that can be quickly annotated by people and then precisely parsed using the current state-of-the-art techniques. Take a look at a couple English sentences and corresponding ULFs.

• Could you dial for me?
(((pres could.aux-v) you.pro (dial.v {ref1}.pro

((if.ps (I.pro ((cf were.v) (= you.pro))))

The dot-extensions .n, .v, .a, .p, .aux-s, and .pro are named in relation to their syntactic part-of-speech correspondents (nouns, verbs, adjectives, etc.). Furthermore, if you’re familiar with constituency parses, you might have noticed that the general structures of these formulas have a lot in common with them. For example, “for me” makes a single constituent, which is a prepositional phrase in constituency trees. Similarly, “dial for me”, “will be able to succeed” are both single constituents that correspond to verb phrases. This sort of correspondence means that we can expect annotating and learning parsers for ULFs shouldn’t be too much of a stretch beyond constituency parsing, for which research has been very successful.
Despite the surface similarity, ULFs are not syntax. The underlying Episodic Logic type system means that there are specific formal meanings and restrictions to the compositions in these formulas. .pro corresponds to individuals in the domain of discourse, whereas .n, .a, and .v correspond to predicates of varying adicity. This is why operators like adv-a are necessary for shifting the types appropriately (e.g. in the case of adv-a, it maps a predicate to a predicate modifier). ULFs are useful both for further resolution of ambiguity towards full Episodic Logic (as the name ULF suggests, one of these resolution steps is scoping) and immediate inference from ULFs. The closeness of ULF to syntax allows it to be used in Natural Logic-like inferences, which are inference derived from syntactic structure, polarity context, and specificity-relations between words and phrases. The semantic types of ULFs also allows it to make forward inferences in a manner similar to Episodic Logic, while attending to the locations of remaining ambiguity.