Non Deterministic Logic Programs
This work addresses the need for formal frameworks in AI domains like planning and optimization, but it appears incremental as it builds upon existing deterministic logic programming semantics.
The authors tackled the problem of representing and reasoning about non-deterministic applications by introducing a logic programming framework with declarative and fixpoint semantics, extending it with non-monotonic negation and defining stable and well-founded model semantics that subsume deterministic versions and apply to conditional planning.
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.