# A Complete Calculus for Possibilistic Logic Programming with Fuzzy Propositional Variables

arXiv: https://arxiv.org/abs/1301.3832 · HTML: https://mlsanity.com/paper/1301.3832/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 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)

In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is value in the unit interval [0,1] which denotes a lower bound on the belief on A in terms of necessity measures. Belief states are modeled by possibility distributions on the set of all many-valued interpretations. In this framework, (i) we define a syntax and a semantics of the general underlying uncertainty logic; (ii) we provide a modus ponens-style calculus for a sublanguage of Horn-rules and we prove that it is complete for determining the maximum degree of possibilistic belief with which a fuzzy propositional variable can be entailed from a set of formulas; and finally, (iii) we show how the computation of a partial matching between fuzzy propositional variables, in terms of necessity measures for fuzzy sets, can be included in our logic programming system.