Non-monotonic Negation in Hybrid Probabilistic Logic Programs

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 nonmonotonic 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.