Epistemic logic meets epistemic game theory: a comparison between multi-agent Kripke models and type spaces
Epistemic logic meets epistemic game theory: a comparison between multi-agent Kripke models and type spaces
复制标题
认知逻辑遇见认知博弈论：多主体 Kripke 模型与类型空间之间的比较
作者：
P. Galeazzi;E. Lorini
在文献中，至少有两种主要的形式结构来处理互动认识论的情况：克里普克模型和类型空间。如许多论文中所示（参见Aumann和Brandenburger in Econometrica 36：1161 - 1180，1995; Baltag等人in Synthese 169：301 - 333，2009; Battigalli和Bonanno in Res Econ 53（2）：149 - 225，1999; Battigalli和Siniscalchi in J Econ Theory 106：356 - 391，2002; Klein和Pacuit in Stud Log 102：297 - 319，2014; Lorini in J Philos Log 42（6）：863 - 904，2013），这两个框架都可以用于表达博弈论中解概念的认识条件。本文的主要结果是一个正式的比较两者之间的语义等价的声明，就两个不同的逻辑系统：一个doxastic逻辑的信仰和知识，doxastic逻辑的信仰和知识。此外，这些逻辑的两个等价的Kripke语义和类型空间语义的声音和完整的公理化。最后，给出了结果的概率推广。本文的另一个结果是Belnap及其同事对信念和知识的认识论-doxastic逻辑与STIT逻辑（"看到它"的逻辑）之间关系的研究（面向未来：我们不确定世界中的代理人和选择，2001年）。
In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers (see Aumann and Brandenburger in Econometrica 36:1161–1180, 1995; Baltag et al. in Synthese 169:301–333, 2009; Battigalli and Bonanno in Res Econ 53(2):149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42(6):863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison between the two and a statement of semantic equivalence with respect to two different logical systems: a doxastic logic for belief and an epistemic–doxastic logic for belief and knowledge. Moreover, a sound and complete axiomatization of these logics with respect to the two equivalent Kripke semantics and type spaces semantics is provided. Finally, a probabilistic extension of the result is also presented. A further result of the paper is a study of the relationship between the epistemic–doxastic logic for belief and knowledge and the logic STIT (the logic of “seeing to it that”) by Belnap and colleagues (Facing the future: agents and choices in our indeterminist world, 2001).