论文标题
抽象群体的常识
Common Knowledge of Abstract Groups
论文作者
论文摘要
认识论逻辑通常会谈论个人代理人或明确列出的代理人的知识。但是，通常希望表达对给定财产指定的代理人群体的了解，例如“经济学家之间的常识”。我们引入了这种常识的逻辑，我们将其称为抽象群体认识论逻辑（AGEL）。也就是说，Agel为我们保持通用的单独代理逻辑中概念给定的代理人组的常识运算符，其中一种可能的代理逻辑是ALC。我们表明，Agel是指数算成的，其下限是通过从标准组认知逻辑中降低而建立的，并且上限是由嵌入到整个$ $ $ $ calculus中的可满足性嵌入的上限。进一步的主要结果包括有限的型号属性（全$ $ -Calculus不享受）和完整的公理化。
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.
