Coalition and Epistemic Logic: an Intensional Approach to groups

联盟和认知逻辑：群体的内涵方法

• 批准号: 499583844
• 负责人: Professor Dr. Olivier Roy
• 金额: --
• 依托单位: Institute of Computer Sciences
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/499583844?language=en
• 关键词: Coalition; Epistemic; Logic; Intensional; Approach

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.

CELIA项目将提升群体知识、信仰和行动逻辑模型中一个重要但迄今为止在很大程度上被忽视的理想化：我们所说的群体“扩展”观点。在绝大多数的贡献，认识，doxastic，和联盟逻辑，一个组确实减少到其扩展，即，其成员的集合。这有一个直接但违反直觉的后果，即当群体的成员身份发生变化时，群体也会改变身份，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。企业，非正式团队，甚至松散的群体通常仍然存在，即使他们获得或失去成员，所有成员的身份很少，如果有的话，在任何中等规模的群体中是共同的知识。为了解除这种理想化，CELIA将研究群体的“内涵”观点，它放松了群体成员资格和群体身份之间的关系，并将其应用于认识论，doxastic，和联盟逻辑，其中集体发挥关键作用。CELIA将分为三个子项目。第一个分项目将研究在群体内涵观点下集体认识态度的逻辑性质，一方面侧重于群体的具体代数或关系运算，另一方面侧重于逻辑上并非无所不知的群体。第二个子项目将研究集体记忆，一旦内涵群体被考虑在内。特别是，它将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。第三个子项目将从内涵的角度重新审视联盟逻辑和研究群体的代理权力。特别是，它将考虑如何典型的表现定理，所谓的可玩的有效性功能的变化时，intensional集团与特定的代数结构被引入。这些发现将允许更自然的应用逻辑模型的问题，集体记忆，集体行动，集体责任。CELIA还依赖于捷克-德国团队，该团队在与拟议研究相关的主题上有着富有成效的合作记录，包括最近的工作为第一个子项目奠定了基础，以及成功完成了第一个DFG-GACR非经典认知和动态逻辑研究资助。