Assigment:Building Events and Temporal Logic

Assignment
Email your answers to Greg and James before class on Feb 18th. We will spend some time discussing the ideas you had in class.


To explore the connections between the readings, try to axiomatize the templates in the reading verb meanings paper in Allen’s temporal logic.

[x ACT <manner>]
[x <state>]
[BECOME [x ]
[[x ACT <manner>] CAUSE [BECOME [y <state>]]
[x CAUSE [BECOME [y <state>]]]

Your axioms should be of the form in the paper. Here are analyses of the basic cases to get you started:
The event class [x ACT <manner>] could be represented as a process type ACT(x, <manner>), and when realized at time T0, it is asserted by the proposition



OCCURRING(ACT(x, <manner>), T0)

As a concrete example, “jack swept (over time t)” is OCCURRING(SWEEP(Jack), t)

The event class [x <state>] corresponds to the state types, and the corresponding formula in the temporal logic would be

HOLDS(<state>(x), t).
Thus, “jack is happy” over time T1 would be
HOLDS(HAPPY(Jack), T1)
 
These two are in some sense “primitive” and don’t have axioms defining their general structure. The remaining three, however, can be axiomatized much in the manner that the event of doing something TWICE is defined in Allen (fifth page in paper).
You’ll need to make some assumptions. Identify and justify them.