# Common Knowledge of Abstract Groups

arXiv: https://arxiv.org/abs/2211.16284 · HTML: https://mlsanity.com/paper/2211.16284/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 23 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 3 of 3)

- [Two variable fragment of Term Modal Logic](https://mlsanity.com/paper/1904.10260/) (2019)
- [Revisiting Epistemic Logic with Names](https://mlsanity.com/paper/2106.11493/) (2021)
- [Probabilistic annotations for protocol models](https://mlsanity.com/paper/2108.03901/) (2021)

## Abstract (arXiv)

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.