Incollection,
Answer Set Programming and S4
(2004)
Abstract
We develop some ideas in order to obtain a nonmonotonic reasoning system based on the modal logic S4. As a consequence we show how to express the well known answer set semantics using a restricted fragment of modal formulas. Moreover, by considering the full set of modal formulas, we obtain an interesting generalization of answer sets for logic programs with modal connectives. We also depict, by the use of examples, possible applications of this inference system.It is also possible to replace the modal logic S4 with any other modal logic to obtain similar nonmonotonic systems. We even consider the use of multimodal logics in order to model the knowledge and beliefs of agents in a scenario where their ability to reason about each other's knowledge is relevant. Our results clearly state interesting links between answer sets, modal logics and multi-agent systems.
