Reducing Fuzzy Answer Set Programming to Model Finding in Fuzzy Logics

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).

💡 Research Summary

The paper “Reducing Fuzzy Answer Set Programming to Model Finding in Fuzzy Logics” addresses the lack of efficient solvers for fuzzy answer set programming (FASP), a formalism that extends classical answer set programming (ASP) with multi‑valued truth degrees. The authors propose a systematic translation of FASP programs into fuzzy logical theories whose models correspond exactly to the answer sets of the original programs, thereby enabling the use of existing fuzzy SAT/SMT solvers.

The work begins with a concise review of fuzzy logical operators: t‑norms (conjunction), t‑conorms (disjunction), residual implicators (implication), and negators (negation). The authors restrict attention to left‑continuous t‑norms because they guarantee the existence of a residual implicator satisfying the residuation principle (T(x,y) ≤ z iff x ≤ I(y,z)). This restriction is not limiting in practice, as common t‑norms such as minimum, product, and Łukasiewicz satisfy it.

FASP programs are defined as finite sets of ground rules of the form a ← T(b₁,…,bₙ), where a is a literal (either an atom or a constant in