Logical Methods pp 654-704 | Cite as

# 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,

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