Towards the Computation of Stable Probabilistic Model Semantics

Abstract

In [22], a stable model semantics extension of the language of hybrid probabilistic logic programs [21] with non-monotonic negation, normal hybrid probabilistic programs (NHPP), has been developed by introducing the notion of stable probabilistic model semantics. It has been shown in [22] that the stable probabilistic model semantics is a natural extension of the stable model semantics for normal logic programs and the language of normal logic programs is a subset of the language NHPP. This suggests that efficient algorithms and implementations for computing the stable probabilistic model semantics for NHPP can be developed by extending the efficient algorithms and implementation for computing the stable model semantics for normal logic programs, e.g., SMODELS [17]. In this paper, we explore an algorithm for computing the stable probabilistic model semantics for NHPP along with its auxiliary functions. The algorithm we develop is based on the SMODELS [17] algorithms. We show the soundness and completeness of the proposed algorithm. We provide the necessary conditions that these auxiliary functions have to satisfy to guarantee the soundness and completeness of the proposed algorithm. This algorithm is the first to develop for studying computational methods for computing the stable probabilistic models semantics for hybrid probabilistic logic programs with non-monotonic negation.