Non-monotonic Negation in Hybrid Probabilistic Logic Programs

Abstract

In [23], a new Hybrid Probabilistic Logic Programs framework has been proposed, and a new semantics has been developed to enable encoding and reasoning about real-world applications. In this paper, the language of Hybrid Probabilistic Logic Programs framework of [23] is extended to allow non-monotonic negation, and two alternative semantics are defined: stable probabilistic model semantics and probabilistic well-founded semantics. Stable probabilistic model semantics and probabilistic well-founded semantics generalize stable model semantics and well-founded semantics of traditional normal logic programs, and they reduce to the semantics of original Hybrid Probabilistic Logic programs framework of [23] for programs without negation. It is the first time that two different semantics for Hybrid Probabilistic Programs with non monotonic negation as well as their relationships are described. This development provides a foundational ground for developing computational methods for computing the proposed semantics. Furthermore, it makes it clearer how to characterize non-monotonic negation in probabilistic logic programming frameworks for commonsense reasoning.