Representation and inference with consistent temporal propositions

Abstract

A b s t r a c t . Reasoning with temporal information is essential in Artificial Intelligence. We consider a knowledge base where the internal representation language deals with temporally qualified propositions and constraints on the ordering of time points. As temporal information is typically partial, a representation including constraSnts on the order of temporal objects is particularly suited. Temporal statements associate maximal intervals to basic atemporal propositions. Queries posed to a knowledge base which includes facts and rules use deduction to explore its consequences and abduction to generate consistent hypotheses. The inference system relies on a set of constraint primitives providing temporal consistency both for points and for intervals. The relevant aspects of the temporal framework axe the underlying propositional language, the abductive derivation procedure and the f~cility of built-in constrMnt handling. The abductive procedure in the inference system provides the strategy for completing paxtial information in order to produce informative answers. The integration of constraint solving with abduction allows a query oriented generation of answers where the enforcement of constraints is efficiently performed. I n t r o d u c t i o nIn most approaches in AI the representation of temporal objects is basically constituted by a proposition and an associated temporal extent [1,6,10]. This corresponds to adopting a very simple temporal ontology. The internal language considered here is based on this ontology, incorporating a feature that is also treated as basic: the intervals for the same proposition are maximal, and therefore disjoint. Briefly, there are two reasons for such an assumption: first, it is intuitively correct to view a proposition in time as a set of disjoint intervals; second, from a practical point of view a knowledge base where only intervals of maximal extent stand is more compact and so are the answers to queries.The language of maximal intervals will be referred to in the sequel as MI and a description can be found in [8]. The propositional (plus time) version considers temporal constants, variables, Skolem constants and functions and proposition symbols. The temporal relations { -, >, <, <, >} are used to build constraint