Dempster-Shafer Logic Programs and Stable Semantics

Abstract

Many researchers (e.g. Baldwin [2] and Ishizuka [19]) have observed that the Dempster-Shafer rule of combination, which is at the heart of Dempster-Shafer theory, exhibits non-monotonic behaviour. However, as they focus entirely on operational concerns, two important issues remain unresolved. In [13], Fitting observes that developing a declarative semantics for logic programs based on the Dempster-Shafer rule is an open problem. More importantly, it is unclear how the mode of non-monotonicity demonstrated by the Dempster-Shafer rule is related to well-understood nonmonotonic logics.In this paper we study Dempster-Shafer logic programs (DS-programs for short). We first develop a declarative semantics for such logic programs. This task alone is complicated by the non-monotonic nature of the Dempster-Shafer rule. Then, given a DS-program P, we transform P to a program P whose clauses may contain non-monotonic negations in their bodies. We proceed to present a stable semantics for P, which is a quantitative extension of the stable semantics for classical logic programs with negations. The major result of this paper is that the meaning of a class of DS-program P, as defined by the declarative semantics based on the Dempster-Shafer rule, is identical to the meaning of P, as defined by the stable semantics. This equivalence links the Dempster-Shafer mode of non-monotonicity very firmly to the stable semantics, and thus to other non-monotonic rule systems due to the results provided by Marek et al [27, 28,KeywordsLogic ProgramGround InstanceNonmonotonic LogicFormula FunctionStable SemanticThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.