Non Deterministic Logic Programs

TL;DR

This paper introduces a new logic programming framework called non deterministic logic programs, designed to model and reason about complex real-world applications involving inherent non-determinism, with formal semantics and practical application to planning.

Contribution

It extends existing logic programming semantics to non deterministic contexts, providing a formal foundation and demonstrating application to conditional planning.

Findings

Semantics subsume deterministic stable and well-founded semantics.

Framework effectively models non deterministic applications like planning.

Application to a conditional planning problem demonstrates practical utility.

Abstract

Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially observable Markov decision processes, and conditional planning. We present a logic programming framework called non deterministic logic programs, along with a declarative semantics and fixpoint semantics, to allow representing and reasoning about inherently non deterministic real-world applications. The language of non deterministic logic programs framework is extended with non-monotonic negation, and two alternative semantics are defined: the stable non deterministic model semantics and the well-founded non deterministic model semantics as well as their relationship is studied. These semantics subsume the deterministic stable model semantics and the deterministic well-founded semantics of deterministic normal logic programs, and they reduce to the semantics of deterministic definite logic programs without negation. We show the application of the non deterministic logic programs framework to a conditional planning problem.