An Alternative Proof Method for Possibilistic Logic and its Application to Terminological Logics

TL;DR

This paper introduces an alternative proof method for possibilistic logic that avoids non-termination issues and applies it to a decidable, expressive terminological logic to better handle uncertain knowledge.

Contribution

It proposes a new proof method based on classical entailment tests, extending possibilistic logic to more expressive, decidable terminological logics.

Findings

The new method avoids non-termination in possibilistic resolution.

It successfully extends terminological logics with uncertainty representation.

The approach is both semantically sound and computationally feasible.

Abstract

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree or a necessity degree that expresses to what extent the formula is possibly or necessarily true. Possibilistic resolution yields a calculus for possibilistic logic which respects the semantics developed for possibilistic logic. A drawback, which possibilistic resolution inherits from classical resolution, is that it may not terminate if applied to formulas belonging to decidable fragments of first-order logic. Therefore we propose an alternative proof method for possibilistic logic. The main feature of this method is that it completely abstracts from a concrete calculus but uses as basic operation a test for classical entailment. We then instantiate possibilistic logic with a terminological logic, which is a decidable subclass o f first-order logic but nevertheless much more expressive than propositional logic. This yields an extension of terminological logics towards the representation of uncertain knowledge which is satisfactory from a semantic as well as algorithmic point of view.