Coalition and Epistemic Logic: an Intensional Approach to groups

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The CELIA project will lift a significant, but until now, largely overlooked idealization in logical models of group knowledge, beliefs, and action: what we call the “extensional” view of groups. In the overwhelming majority of contributions to epistemic, doxastic, and coalition logic, a group is indeed reduced to its extension, i.e., the set of its members. This has the immediate but counter-intuitive consequence that groups change identity when their membership changes, and rules out uncertainty regarding who is in a given group. This idealization does not reflect the structure of groups in the intended application of these logical models. Firms, informal teams, or even loose crowds typically remain even if they gain or lose members, and the identity of all members is rarely, if ever, common knowledge in any group of moderate size.To lift this idealization, CELIA will study the “intensional” view of groups, which loosens the relationship between group membership and group identity, and apply it to questions in epistemic, doxastic, and coalition logic where collectives play a crucial role.CELIA will be divided into three sub-projects. The first sub-project will study the logical properties of collective epistemic attitudes under the intensional view of groups by focusing, on the one hand, on specific algebraic or relational operations on groups and, on the other hand, on groups that are not logically omniscient. The second sub-project will study collective memory once intensional groups are taken into account. It will, in particular, study the relation between so-called individual and collective perfect recall, defined using distributed and common knowledge. The third sub-project will re-visit coalition logic and study groups’ agentive powers from an intensional perspective. In particular, it will consider how the canonical representation theorems for so-called playable effectivity functions change when intensional groups with specific algebraic structures are introduced.These findings will allow for more natural applications of logical models to questions of collective memory, collective action, and collective responsibility. CELIA furthermore rests on a Czech-German team that has a strong track record of fruitful collaboration on themes relevant to the proposed research, including recent work laying down the foundations for the first sub-project, and the successful completion of a first DFG-GACR research grant on non-classical epistemic and dynamic logic.