Epistemic Logics of Structured Intensional Groups

TL;DR

This paper develops a general semantic framework for epistemic logics of structured intensional groups, allowing properties defining group membership to vary across possible worlds, and unifies various existing frameworks under this approach.

Contribution

It introduces a comprehensive semantic framework for structured intensional groups, generalizing and unifying previous models in the literature.

Findings

Established a completeness-via-canonicity result.

Showed that several existing frameworks are special cases of the general framework.

Provided a unified semantic foundation for epistemic logics of intensional groups.

Abstract

Epistemic logics of intensional groups lift the assumption that membership in a group of agents is common knowledge. Instead of being represented directly as a set of agents, intensional groups are represented by a property that may change its extension from world to world. Several authors have considered versions of the intensional group framework where group-specifying properties are articulated using structured terms of a language, such as the language of Boolean algebras or of description logic. In this paper we formulate a general semantic framework for epistemic logics of structured intensional groups, develop the basic theory leading to completeness-via-canonicity results, and show that several frameworks presented in the literature correspond to special cases of the general framework.