Common Knowledge of Abstract Groups

TL;DR

This paper introduces AGEL, a logic for expressing common knowledge among groups of agents defined by properties, with complexity results, a finite model property, and a complete axiomatization.

Contribution

It develops AGEL, a novel logic that allows for common knowledge among property-defined groups, extending traditional agent-specific epistemic logics.

Findings

AGEL is EXPTIME-complete.

AGEL has a finite model property.

A complete axiomatization for AGEL is provided.

Abstract

Epistemic logics typically talk about knowledge of individual agents or groups of explicitly listed agents. Often, however, one wishes to express knowledge of groups of agents specified by a given property, as in `it is common knowledge among economists'. We introduce such a logic of common knowledge, which we term abstract-group epistemic logic (AGEL). That is, AGEL features a common knowledge operator for groups of agents given by concepts in a separate agent logic that we keep generic, with one possible agent logic being ALC. We show that AGEL is EXPTIME-complete, with the lower bound established by reduction from standard group epistemic logic, and the upper bound by a satisfiability-preserving embedding into the full $\mu$-calculus. Further main results include a finite model property (not enjoyed by the full $\mu$-calculus) and a complete axiomatization.