Partial models and logic programming (Q1094151)

The author carries on investigations of the treatment of negation in logic programming with negation initiated in his earlier work [J. Logic Programming 2, 295--312 (1985; Zbl 0589.68011)]. Essential feature is the treatment of partial models containing statements not only about truth of some (not necessarily atomic) formulas but also about their falsity. The model extension operation considered is based on the treatment of rules \(L\leftarrow A\) as equivalences. Several types of fixed point semantics for logic programs are proposed and one of them turns out to be recursively enumerable (weak semantics). A corresponding system of semantic tableaux is constructed such that the rules corresponding to the rules of the logic program remind familiar modal rules.