On modal presentation of explosive and paraconsistent equilibrium logic
On modal presentation of explosive and paraconsistent equilibrium logic
Siberian Electronic Mathematical Reports, 22, 1, pp. 479-499 (2025)
Abstract:
Fariñas del Cerro, Herzig and Su proved that the non-monotonic consequence relation determined by Answer Set Semantics (ASP) for logic programs with negation-as-failure can be embedded into a monotonic modal logic via a variation of Gödel-Tarski Translation. This article generalizes the mentioned result to ASP for logic programs with two kinds of negation: negation-as-failure and strong negation and to PAS, the paraconsistent version of ASP admitting answer sets that are inconsistent w.r.t. the strong negation.
Keywords: logic programs, negation-as-failure, strong negation, equilibrium logic, deductive base, temporal logic, equilibrium modal theory.