Common Knowledge of Abstract Groups
This work addresses a limitation in epistemic logics for specifying groups in AI and multi-agent systems, though it is incremental as it builds on existing logics.
The paper tackles the problem of expressing common knowledge among groups defined by properties rather than explicit lists, introducing abstract-group epistemic logic (AGEL) and showing it is EXPTIME-complete, with additional results including a finite model property and complete axiomatization.
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 $μ$-calculus. Further main results include a finite model property (not enjoyed by the full $μ$-calculus) and a complete axiomatization.