Graded Distributed Belief

TL;DR

This paper introduces a new logic for modeling graded distributed beliefs among agents, providing semantics, axiomatization, and decision procedures, with applications to understanding epistemic disagreement.

Contribution

It presents a novel logic of graded distributed belief with semantics based on belief bases, and offers a complete axiomatization and decision procedures including PSPACE-completeness.

Findings

Logic formalizes beliefs with at least strength k

Provides sound and complete axiomatization

Decidability established with PSPACE complexity

Abstract

We introduce a new logic of graded distributed belief that allows us to express the fact that a group of agents distributively believe that a certain fact holds with at least strength k. We interpret our logic by means of computationally grounded semantics relying on the concept of belief base. The strength of the group's distributed belief is directly computed from the group's belief base after having merged its members' individual belief bases. We illustrate our logic with an intuitive example, formalizing the notion of epistemic disagreement. We also provide a sound and complete Hilbert-style axiomatization, decidability result obtained via filtration, and a tableaux-based decision procedure that allows us to state PSPACE-completeness for our logic.