Safe beliefs for propositional theories
The paper presents an extension of answer sets that are called safe beliefs. Safe beliefs allow for the use of arbitrary propositional theories as logic programs. The presented approach allows for the use of even modal or temporal logics as the underlying inference system to produce different semantic operators with additional or extended features. One of the main theorems of the paper shows that any propositional logic that is strictly weaker than classical logic and stronger than intuitionistic logic can be used in the definition of safe beliefs without modifying the resulting semantic operator. Another contribution of the paper is to present a translation that can be used to reduce any propositional theory into the class of augmented logic programs. Other translations can be used to provide a polynomial reduction of arbitrary propositional theories into disjunctive logic programs. Reviewer's remark: The 7th line of p. 66 contains a misprint: the atoms \(b_{m+1},\dots, b_{m+l}\) must be negated.
scientific article; zbMATH DE number 2173066