Reducing Fuzzy Answer Set Programming to Model Finding in Fuzzy Logics

Abstract

In recent years answer set programming has been extended to deal with multi-valued predicates. The resulting formalisms allows for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where many efficient solvers have been constructed, to date there is no efficient fuzzy answer set programming solver. A well-known technique for classical ASP consists of translating an ASP program $P$ to a propositional theory whose models exactly correspond to the answer sets of $P$. In this paper, we show how this idea can be extended to fuzzy ASP, paving the way to implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners. To appear in Theory and Practice of Logic Programming (TPLP).