Clausal logic and logic programming in algebraic domains

Authors:
William C. Rounds;Guo-Qiang Zhang
Affiliations:
Univ. of Michigan, Ann Arbor;Case Western Reserve Univ., Cleveland, OH
Venue:
Information and Computation
Year:
2002

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Abstract

We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introduce a natural declarative semantics and a fixed-point semantics for disjunctive logic programs, and prove their equivalence; finally, we apply our results to give both a syntax and semantics for default logic in any coherent algebraic dcpo. 2001 Elsevier Science