Answer Sets in General Nonmonotonic Reasoning (preliminary report) (1991)
Vladimir Lifschitz and Thomas Y. C. Woo
Languages of declarative logic programming differ 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 ex tended 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 dis tinguishing feature of logic programming in general. As a starting point, we take a trans lation from the language of disjunctive pro grams with negation as failure and classical negation into MBNF---the logic of minimal belief and negation as failure. A class of the ories based on this logic is defined, theories with protected literals, which is syntactically uniform and contains the translations of all programs. We show that theories with pro tected literals have a semantics similar to the answer set semantics used in logic program ming, and investigate the expressiveness of these theories.
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In Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning, pp. 603--614 1991.
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Vladimir Lifschitz Faculty vl [at] cs utexas edu