Semantics for Possibilistic Disjunctive Programs

TL;DR

This paper introduces a possibilistic disjunctive logic programming framework for modeling uncertain, incomplete, and inconsistent information, providing semantics, resolution algorithms, and inconsistency management techniques, demonstrated through a medical example.

Contribution

It presents a novel possibilistic disjunctive logic programming approach with semantics, resolution methods, and inconsistency handling, advancing reasoning under uncertainty.

Findings

Semantic characterization by fixed-point operator

Resolution algorithm for computing models

Inconsistency management via preferences and cuts

Abstract

In this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses which are able to capture incomplete information and incomplete states of a knowledge base at the same time. By considering a possibilistic logic program as a possibilistic logic theory, a construction of a possibilistic logic programming semantic based on answer sets and the proof theory of possibilistic logic is defined. It shows that this possibilistic semantics for disjunctive logic programs can be characterized by a fixed-point operator. It is also shown that the suggested possibilistic semantics can be computed by a resolution algorithm and the consideration of optimal refutations from a possibilistic logic theory. In order to manage inconsistent possibilistic logic programs, a preference criterion between inconsistent possibilistic models is defined; in addition, the approach of cuts for restoring consistency of an inconsistent possibilistic knowledge base is adopted. The approach is illustrated in a medical scenario.