Field Knowledge as a Dual to Distributed Knowledge: A Characterization by Weighted Modal Logic

TL;DR

This paper refines the formal understanding of distributed knowledge by introducing field knowledge as its dual, using weighted modal logic to analyze various group knowledge constructs and their expressivity.

Contribution

It introduces the concept of field knowledge as a dual to distributed knowledge and develops weighted modal logic frameworks for their formal characterization.

Findings

Field knowledge is formally characterized as a dual to distributed knowledge.

Eight weighted modal logics are analyzed for expressivity.

Sound and complete axiomatic systems are developed for these logics.

Abstract

The study of group knowledge concepts such as mutual, common, and distributed knowledge is well established within the discipline of epistemic logic. In this work, we incorporate epistemic abilities of agents to refine the formal definition of distributed knowledge and introduce a formal characterization of field knowledge. We propose that field knowledge serves as a dual to distributed knowledge. Our approach utilizes epistemic logics with various group knowledge constructs, interpreted through weighted models. We delve into the eight logics that stem from these considerations, explore their relative expressivity and develop sound and complete axiomatic systems.