Coalition and Epistemic Logic: an Intensional Approach to groups

CELIA项目将提升一个重要的，但到目前为止，在群体知识、信仰和行动的逻辑模型中，很大程度上被忽视的理想化：我们称之为群体的“外延”观。在对认识论、谬论和联合逻辑的绝大多数贡献中，一个群体确实被简化为它的扩展，即它的成员的集合。这有一个直接但反直觉的结果，即当群体的成员发生变化时，群体的身份也会发生变化，并排除了谁在特定群体中的不确定性。这种理想化并不能反映这些逻辑模型的预期应用程序中的组结构。公司、非正式的团队，甚至松散的群体，即使增加或减少成员，也通常会保留下来，而且在任何中等规模的群体中，所有成员的身份很少（如果有的话）是众所周知的。为了消除这种理想化，CELIA将研究群体的“内涵”观点，这种观点放松了群体成员和群体身份之间的关系，并将其应用于集体发挥关键作用的认识论、悖论和联盟逻辑中的问题。CELIA将分为三个子项目。第一个子项目将通过一方面关注群体的特定代数或关系操作，另一方面关注逻辑上不全知的群体，在群体的内涵观点下研究集体认知态度的逻辑属性。第二个子项目将研究集体记忆，一旦考虑到内部群体。它将特别研究所谓的个人和集体完美回忆之间的关系，用分布式和共同的知识来定义。第三个子项目将重新审视联盟逻辑和研究小组的代理权力从内涵的角度。特别地，它将考虑当引入具有特定代数结构的内涵群时，所谓可玩有效性函数的规范表示定理是如何变化的。这些发现将使逻辑模型更自然地应用于集体记忆、集体行动和集体责任等问题。此外，CELIA还依赖于一个捷克-德国团队，该团队在与拟议研究相关的主题上有着丰硕的合作记录，包括最近为第一个子项目奠定基础的工作，以及成功完成了第一个DFG-GACR关于非经典认知和动态逻辑的研究资助。

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.