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

arXiv: https://arxiv.org/abs/1302.6819 · HTML: https://mlsanity.com/paper/1302.6819/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2013.

## Built on by (most cited first, 2 of 2)

- [A First Polynomial Non-Clausal Class in Many-Valued Logic](https://mlsanity.com/paper/2110.12901/) (2021)
- [The Possibilistic Horn Non-Clausal Knowledge Bases](https://mlsanity.com/paper/2111.07648/) (2021)

## Abstract (arXiv)

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.