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

Answer set programming (ASP) is a form of declarative programming oriented towards difficult search problems. As an outgrowth of research on the use of nonmonotonic reasoning in knowledge representation, it is particularly useful in knowledge-intensive applications. ASP programs consist of rules that look like Prolog rules, but the computational mechanisms used in ASP are different: they are based on the ideas that have led to the creation of fast satisfiability solvers for propositional logic.

In this article, we compare the expressive powers of classes of normal logic programs that are obtained by constraining the number of positive subgoals in the bodies of rules. The comparison is based on the existence/nonexistence of polynomial, faithful, and modular translation functions between the classes. As a result, we obtain a strict ordering among the classes under consideration. Binary programs are shown to be as expressive as unconstrained programs but strictly more expressive than unary programs which, in turn, are (...) strictly more expressive than atomic programs. We also take propositional theories into consideration and prove them to be strictly less expressive than atomic programs. In spite of the gap in expressiveness, we develop a faithful but non-modular translation function from normal programs to propositional theories. We consider this as a breakthrough due to sub-quadratic time complexity |). Furthermore, we present a prototype implementation of the translation function and demonstrate its promising performance with SAT solvers using three benchmark problems. (shrink)