---
title: "Interval-Based Possibilistic Logic"
authors:
  - "Salem Benferhat"
  - "Julien Hué"
  - "Sylvain Lagrue"
  - "Julien Rossit"
doi: "10.5591/978-1-57735-516-8/IJCAI11-132"
url: "https://ijcai.org/proceedings/2011/132"
pdf: "https://ijcai.org/proceedings/2011/0132.pdf"
venue: "Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence"
year: 2011
pages: "750-754"
track: ""
keywords:
---

# Interval-Based Possibilistic Logic

Salem Benferhat, Julien Hué, Sylvain Lagrue, Julien Rossit

*Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence*, pages 750-754. DOI: [10.5591/978-1-57735-516-8/IJCAI11-132](https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-132)

## Abstract

Possibilistic logic is a well-known framework for dealing with uncertainty and reasoning under inconsistent knowledge bases. Standard possibilistic logic expressions are propositional logic formulas associated with positive real degrees belonging to [0,1]. However, in practice it may be difficult for an expert to provide exact degrees associated with formulas of a knowledge base. This paper proposes a flexible representation of uncertain information where the weights associated with formulas are in the form of intervals. We first study a framework for reasoning with interval-based possibilistic knowledge bases by extending main concepts of possibilistic logic such as the ones of necessity and possibility measures. We then provide a characterization of an interval-based possibilistic logic base by means of a concept of compatible standard possibilistic logic bases. We show that interval-based possibilistic logic extends possibilistic logic in the case where all intervals are singletons. Lastly, we provide computational complexity results of deriving plausible conclusions from interval-based possibilistic bases and we show that the flexibility in representing uncertain information is handled without extra computational costs.