Entailments in finite-state temporality

The “surge in use of finite-state methods” ([10]) in computational linguistics has largely, if not completely, left semantics untouched. The present paper is directed towards correcting this situation. Techniques explained in [1] are applied to a fragment of temporal semantics through an approach we call finite-state temporality . This proceeds from the intuition of an event as “a series of snapshots” ([15]; see also [12]), equating snapshots with symbols that collectively form our alphabet. A sequence of snapshots then becomes a string over that alphabet, evoking comic/film strips. Jackendoff has, among others, objected to conceptualizing events in terms of snapshots ([8]). To counter these objections, we step up from events-as-strings to event-typesas-regular languages ([5, 6]), recognizing the need for variable granularity. Beyond the introduction of disjunction implicit in the step from a single string up to a set of strings, we obtain a useful logic from the regular operations and a careful choice of the snapshots (constituting our alphabet). To a first approximation, a snapshot is simply a set of formulas, or fluents, described to hold at some point in time. These sets are not to be construed as exhaustive: the absence of a fluent φ from a set α need not mean that φ does not hold at the time described by α — only that α does not describe φ as holding at that time. Hence, a snapshot α is at least as informative as β if β is a subset of α, β ⊆ α. We define a subsumption relation D in section 2 that extends this notion of underspecification to strings of the same length and more generally, to languages. Building on D, we modify Koskenniemi’s restriction operator => ([1], page 64) in section 3 to express various entailments as regular languages. Examples include the constraints (1) and (2) on our alphabet.