Graded Distributed Belief
Emiliano Lorini, Dmitry Rozplokhas
TL;DR
This paper extends epistemic reasoning to graded distributed beliefs by modeling agents' explicit beliefs with graded belief bases and deriving group beliefs through weighted base merging. It develops a modal language with graded distributed belief operators, analyzes multiple semantic characterizations (MAGBM, NGDM, QNGDM) and proves their equivalence, and provides a sound and complete Hilbert-style axiomatization. A tableaux-based decision procedure is shown to be PSPACE-complete, ensuring practical decidability. The work also includes a concrete example of epistemic disagreement and outlines directions for future work, including ordinal grades, qualitative variants, and dynamic belief-base changes.
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.