Game semantics of disjunctive logic programming

Denotational semantics of logic programming and its extensions (by allowing negation, disjunctions, or both) have been studied thoroughly for many years. In 1998, game semantics were given to definite logic programs by Di Cosmo, Loddo, and Nicolet, and a few years later they were extended to deal with negation by Rondogiannis and Wadge. Both approaches were proven equivalent with the traditional denotational semantics. In this paper we define the game semantics for disjunctive logic programs and prove soundness and completeness with respect to the minimal model semantics of Minker. The overall development has been influenced by the games studied for PCF and functional programming in general, in the style of Abramsky–Jagadeesan–Malacaria and Hyland–Ong.