Common Knowledge of Abstract Groups

Humml M, Schröder L (2023)

Publication Language: English

Publication Type: Conference contribution

Publication year: 2023

Journal

Proceedings of the AAAI Conference on Artificial Intelligence Association for the Advancement of Artificial Intelligence

Series: AAAI Conference on Artificial Intelligence

Book Volume: 37

Pages Range: 6434-6441

Event location: Washington DC US

Issue: 5

Journal Issue: 5

DOI: 10.1609/aaai.v37i5.25791

Open Access Link: https://ojs.aaai.org/index.php/AAAI/article/view/25791/25563

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 µ-calculus. Further main results include a finite model property (not enjoyed by the full µ-calculus) and a complete axiomatization.

Authors with CRIS profile

Merlin Humml Lehrstuhl für Informatik 8 (Theoretische Informatik) Lutz Schröder Lehrstuhl für Informatik 8 (Theoretische Informatik)

Related research project(s)

Cyberkriminalität und forensische Informatik (Cybercrime) Oct. 1, 2019 - March 31, 2024 Reconstructing Arguments from Newsworthy Debates (RAND) Jan. 1, 2021 - Dec. 31, 2023

How to cite

APA:

Humml, M., & Schröder, L. (2023). Common Knowledge of Abstract Groups. In Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence Thirteenth Symposium on Educational Advances in Artificial Intelligence (pp. 6434-6441). Washington DC, US.

MLA:

Humml, Merlin, and Lutz Schröder. "Common Knowledge of Abstract Groups." Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence Thirteenth Symposium on Educational Advances in Artificial Intelligence, Washington DC 2023. 6434-6441.

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