Reasoning with maximal time intervals

Abstract

The ability to deal with partial knowledge is particularly important in a temporal domain. We describe a temporal language that accounts for incompletely specified temporal information about propositions. Temporal terms in the language denote time instants and inequality constraints are used to keep incomplete information about their order. The language is semantically based on the notion of maximal interval, the denotation of a proposition being a set of maximal intervals where it holds. The adequacy of maximal intervals for temporal knowledge representation has been justified elsewhere [5]. In a partial KB, abduction on the temporal order is generally needed to answer a query, and the answer is then conditional on the abduced facts. To comply with the intended semantics, an implicit form of temporal consistency has to be enforced, and this presents the main challenge to the design of the inference mechanism. We present here the syntax and declarative semantics of a propositional version of the language of maximal intervals and a first discussion of the problems in designing an inference system adequate to work with this temporal framework. Rather than presenting a complete solution, we discuss several approaches.

This research was supported by Portuguese JNICT project PEROLA.

Owns a scholarship from INIC.