Temporal Answer Set Programming

Abstract

Answer Set Programming (ASP) has become a popular way for representing different kinds of scenarios from knowledge  representation in Artificial Intelligence. Frequently, these scenarios
involve a temporal component which must be considered. In ASP, time is usually represented as a variable whose values are defined by an extensional predicate with a finite domain. Dealing with a finite temporal interval has some disadvantages. First, checking the existence of a plan is not possible and second, it also makes difficult to decide whether two programs are strongly equivalent.
If we extend the syntax of Answer Set Programming by using temporal operators from temporal modal logics, then infinite time can be considered, so the aforementioned disadvantages can be overcome. This extension constitutes, in fact, a formalism called Temporal Equilibrium Logic, which is based on Equilibrium Logic (a logical characterisation of ASP).
Although recent contributions have shown promising results, Temporal Equilibrium Logic is still a novel paradigm and there are many gaps to fill. Our goal is to keep developing this paradigm, filling those gaps and turning it into a suitable framework for temporal reasoning.