Contracted Temporal Equilibrium Logic

Abstract

The stable model semantics of logic programs has been characterized by Equilibrium Logic, which is a non-monotonic formalism that selects models from the (monotonic) intermediate logic of Here-and-There. It provides stable models for arbitrary propositional formulas and has been fruitfully extended to different modal languages. Among them are theories in the syntax of Linear-Time Temporal Logic (LTL), giving rise to Temporal Equilibrium logic (TEL) based on Temporal Here-and-There (THT). In TEL, models are selected that minimize truth among THT traces of the same length. In this paper, we consider a selection that in addition may reduce the number of transitions in a trace, intuitively forming a contraction of it. We thus introduce contracted THT and contracted TEL on top of a model selection on a logical basis. The resulting c-stable models can be viewed as stable models in TEL that can not be summarized into a smaller trace. We illustrate contraction on several examples related to logic programming and explore several properties, like the relation to TEL and LTL, and in particular the connection to the LTL property of stuttering.