Coalition and Epistemic Logic: an Intensional Approach to groups

西莉亚项目将提升一个重要的、但到目前为止在很大程度上被忽视的群体知识、信念和行动的逻辑模型中的理想化：我们所称的群体的“外延”观点。在认识论、道克论和联盟逻辑的绝大多数贡献中，一个群体实际上被简化为它的外延，即它的成员的集合。这产生了一个直接但违反直觉的后果，即当成员发生变化时，群体会改变身份，并排除了关于谁在给定群体中的不确定性。这种理想化并不反映这些逻辑模型的预期应用中的群体结构。公司、非正式团队，甚至松散的人群，即使他们获得或失去了成员，通常也会留下来，而且所有成员的身份在任何中等规模的组织中都很少是常识。为了提升这种理想化，西莉亚将研究群体的“内涵”观点，该观点松散了群体成员和群体认同之间的关系，并将其应用于集体起关键作用的认识论、道克论和联盟逻辑中的问题。CELIA将分为三个子项目。第一个子项目将研究群体内在观下集体认知态度的逻辑性质，一方面集中在对群体的特定代数或关系运算上，另一方面集中在逻辑上不全知的群体上。第二个子项目将研究集体记忆，一旦考虑到内涵群体。它将特别研究所谓的个人和集体完美回忆之间的关系，使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，并从内涵的角度研究群体的代理权力。特别是，它将考虑当具有特定代数结构的内涵群被引入时，所谓的可玩有效性函数的正则表示定理如何改变。这些发现将允许逻辑模型更自然地应用于集体记忆、集体行动和集体责任的问题。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卓有成效的合作记录，包括最近为第一个分项目奠定基础的工作，以及成功完成DFG-GACR关于非经典认知和动态逻辑的第一笔研究拨款。

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.