---
title: "A Fuzzy Modal Logic for Belief Functions"
authors:
  - "Lluís Godo"
  - "Petr Hájek"
  - "Francesc Esteva"
doi: ""
url: "https://ijcai.org/proceedings/2001/99"
pdf: "https://ijcai.org/proceedings/2001/0099.pdf"
venue: "Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence"
year: 2001
pages: "723-731"
track: ""
keywords:
---

# A Fuzzy Modal Logic for Belief Functions

Lluís Godo, Petr Hájek, Francesc Esteva

*Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence*, pages 723-731.

## Abstract

In this paper we introduce a new logical approach to reason explicitly about Dempster-Shafer belief functions. We adopt the following view: one just starts with Boolean formulas and a belief function on them; the belief of is taken to be the truth degree of the (fuzzy) proposition 
 standing for “is believed”. For our complete axiomatization (Hylbert-style) we use one of the possible definitions of belief, namely as probability of (modal) necessity. This enables us to define a logical system combining the modal logic S5 with an already proposed fuzzy logic approach to reason about probabilities. In particular, our fuzzy logic is the logic Ł   which puts Lukasiewicz and Product logics together.