Resolution and Logic Programming in Algebraic Domains: Negation and Defaults

W.C. Rounds and G.-Q. Zhang have recently proposed to study a form of disjunctive logic programming generalized to algebraic domains [RZ01]. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with negative information, i.e. the implicit or explicit absence of bits of information. These investigations will naturally lead to a form of default reasoning which is strongly related to logic programming with answer sets or stable models, which has recently created much interest amongst artificial intelligence researchers concerned with knowledge representation and reasoning.