Loop Formulas for Splitable Temporal Logic Programs

In this paper, we study a method for computing temporal equilibrium models, a generalisation of stable models for logic programs with temporal operators, as in Linear Temporal Logic (LTL). To this aim, we focus on a syntactic subclass of these temporal logic programs called splitable and whose main property is satisfying a kind of “future projected” dependence present in most dynamic scenarios in Answer Set Programming (ASP). Informally speaking, this property can be expressed as “past does not depend on the future.” We show that for this syntactic class, temporal equilibrium models can be captured by an LTL formula, that results from the combination of two well-known techniques in ASP: splitting and loop formulas. As a result, an LTL model checker can be used to obtain the temporal equilibrium models of the program.