Answer Sets in General Nonmonotonic Reasoning (Preliminary Report)

Languages of declarative logic programming diier from other modal nonmonotonic formalisms by lack of syntactic uniformity. For instance, negation as failure can be used in the body of a rule, but not in the head; in disjunctive programs, disjunction is used in the head of a rule, but not in the body; in extended programs, negation as failure can be used on top of classical negation, but not the other way around. We argue that this lack of uniformity should not be viewed as a distinguishing feature of logic programming in general. As a starting point, we take a translation from the language of disjunctive programs with negation as failure and classical negation into MBNF|the logic of minimal belief and negation as failure. A class of theories based on this logic is deened, theories with protected literals, which is syntactically uniform and contains the translations of all programs. We show that theories with protected literals have a semantics similar to the answer set semantics used in logic programming , and investigate the expressiveness of these theories.