Possibilistic Answer Set Programming Revisited

TL;DR

This paper revisits possibilistic answer set programming (PASP), proposing a new semantics based on possibilistic logic, and introduces a generalized Gelfond-Lifschitz reduct compatible with standard ASP solvers.

Contribution

It develops a more intuitive and well-founded semantics for PASP by characterizing answer sets via possibilistic logic and provides a syntactic reduct for implementation.

Findings

New semantics for PASP based on possibilistic logic

A generalized Gelfond-Lifschitz reduct for PASP

Framework compatible with existing ASP solvers

Abstract

Possibilistic answer set programming (PASP) extends answer set programming (ASP) by attaching to each rule a degree of certainty. While such an extension is important from an application point of view, existing semantics are not well-motivated, and do not always yield intuitive results. To develop a more suitable semantics, we first introduce a characterization of answer sets of classical ASP programs in terms of possibilistic logic where an ASP program specifies a set of constraints on possibility distributions. This characterization is then naturally generalized to define answer sets of PASP programs. We furthermore provide a syntactic counterpart, leading to a possibilistic generalization of the well-known Gelfond-Lifschitz reduct, and we show how our framework can readily be implemented using standard ASP solvers.