A Theorem Prover for Prioritized Supernormal Defaults

We present a top-down theorem prover for arbitrary clauses and defaults of the form true : δ/δ (supernormal defaults) with priorities. This especially allows to specify the perfect model semantics for stratified programs, but it includes also disjunctions, classical negation and more general defaults than the usual negations. In this paper, we concentrate on the handling of the priorities and consider only the credulous approach to multiple extensions. But the ideas from [Bra92a] can be used to get the skeptical and the careful semantics corresponding to prioritized circumscription and an extension of the GCWA. The most interesting aspect of our work is that we are able to incrementally check the applicability of the defaults during the main proof (via our notion of partial extensions). Other theorem provers for prioritized circumscription [BG89] had to postpone this test into a second phase. So our approach seems to be closer to the usual “negation as failure” rule which evaluates negated literals when they occur in the proof. A prototype of the theorem prover has been implemented in Prolog.