Disjunctive logic programs, answer sets, and the cut rule

Abstract In Minker and Rajasekar (J Log Program 9(1):45–74, 1990), proposed a semantics for negation-free disjunctive logic programs that offers natural generalisation of the fixed point definite programs. We show this can be further generalised with classical negation, in constructive modal-theoretic framework where rules are built from claims hypotheses , namely, formulas form $$\Box \varphi $$ □ φ $$\Diamond \Box ◊ $$\varphi is literal, respectively, yielding “base semantics” general Model-theoretically, base expressed terms notion logical consequence. It has complete proof procedure based on cut rule. Usually, alternative amount to particular interpretation nonclassical negation as “failure derive.” The counterpart our complement original program set required satisfy specific conditions, apply resulting set. demonstrate approach answer semantics. purely mainly three ways. First, it uses unique negation. Second, advocates computation consequences rather than models. Third, makes no reference preferred or minimal interpretation.