---
title: "Compatible-Based Conditioning in Interval-Based Possibilistic Logic"
authors:
  - "Salem Benferhat"
  - "Amélie Levray"
  - "Karim Tabia"
  - "Vladik Kreinovich"
doi: ""
url: "https://ijcai.org/proceedings/2015/393"
pdf: "https://ijcai.org/proceedings/2015/0393.pdf"
venue: "Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence"
year: 2015
pages: "2777-2782"
track: "Special Track on Knowledge Representation and Reasoning"
keywords:
---

# Compatible-Based Conditioning in Interval-Based Possibilistic Logic

Salem Benferhat, Amélie Levray, Karim Tabia, Vladik Kreinovich

*Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence*, pages 2777-2782.

## Abstract

Interval-based possibilistic logic is a flexible setting extending standard possibilistic logic such that each logical expression is associated with a sub-interval of [0,1]. This paper focuses on the fundamental issue of conditioning in the interval-based possibilistic setting. The first part of the paper first proposes a set of natural properties that an interval-based conditioning operator should satisfy. We then give a natural and safe definition for conditioning an interval-based possibility distribution. This definition is based on applying standard min-based or product-based conditioning on the set of all associated compatible possibility distributions. We analyze the obtained posterior distributions and provide a precise characterization of lower and upper endpoints of the intervals associated with interpretations. The second part of the paper provides an equivalent syntactic computation of interval-based conditioning when interval-based distributions are compactly encoded by means of interval-based possibilistic knowledge bases. We show that interval-based conditioning is achieved without extra computational cost comparing to conditioning standard possibilistic knowledge bases.