Aspect and Interval Tense Logic

Speaker: Dr Miguel Leith
Date: 4th February 1999
Place: Room 433 Huxley Building
Time: 1:30 p.m.

Abstract

Linguistic phenomena of tense and aspect have been investigated in a
great deal of theoretical work in linguistics,
philosophy and computer science. Modern tense logics, established by
Prior, are part of this effort.
Point tense logics offer an intuitive representation of tense but lack
the expressiveness to represent many aspectual structures. Interval
tense logics offer more expressiveness but in the general case can be
computationally intractable.  From a linguistic perspective there is the
problem of precisely how to formalise the aspectual structures, such as
a culmination and a culminated process.

In this paper we define a computationally tractable augmented fragment
of Halpern and Shoham's interval tense logic HS and apply it to
represent a core set of aspectual structures and the temporal readings
of a number of example sentences. We define satisfiability of the
fragment with respect to timeline models, and two procedures, one for
constructing the minimal timelines that satisfy a formula and one for
checking semantic entailments between one formula and another by
comparing their timelines. We apply the former to compute models of
temporal readings and the latter to check a number of linguistic
entailments.