an:00036731
Zbl 0771.68084
Vauzeilles, J.; Strauss, A.
Intuitionistic three-valued logic and logic programming
EN
RAIRO, Inform. Th??or. Appl. 25, No. 6, 557-587 (1991).
00159311
1991
j
68Q55 68N17
semantics of logic programs; Trivalued sequent calculus; SLD-resolution; Clark's completion; semantics for programs with negation; SLDNF- resolution
Summary: We study the semantics of logic programs with the help of trivalued logic, introduced by \textit{J. Y. Girard} [Three-Valued Logic and Cut- Elimination: The Actual Meaning of Takeuti's Conjecture, Diss. Math., Warszawa, 45 p. (1976; Zbl 0357.02027)].
Trivalued sequent calculus enables to extend easily the results of classical SLD-resolution to trivalued logic. Moreover, if one allows negation in the head and in the body of Horn clauses, one obtains a natural semantics for such programs regarding these clauses as axioms of a theory written in the intuitionistic fragment of that logic.
Finally, we define in the same calculus an intuitionistic trivalued version of Clark's completion, which gives us a declarative semantics for programs with negation in the body of the clauses, the evaluation method being SLDNF-resolution.
Zbl 0357.02027