Study of multi-modal logics and its application to game theory

在其他多模态逻辑中，我们主要讨论了多智能体认知逻辑。我们可以利用多智能体认知逻辑来描述人与人之间的认知推理，从而将其应用到博弈论中。作为应用，我们主要尝试分析博弈论的决策过程。运用多模态认知逻辑的思想，使我们对认知逻辑与博弈论的关系有了新的认识。对今后的研究提出了许多建议。我们发现人与人之间的认知推理对“浅深度”的限制是有限理性的一个重要方面。在这个IGEF系统中，我们可以利用思维序列来描述这种限制。我们的系统使我们能够将人际认知推理与其他能力“隔离”开来，并将有限理性视为对人际认知推理能力的限制。此外，我们成功地构造了这种多模态认知逻辑的扩展kripke型语义。主要的和相关的结果如下：构造了多智能体认知逻辑的IGEF系统，该系统具有人与人之间的认知推理对浅深度的限制。这些系统使我们能够在博弈论情境中描述人际认知推理的内容成本。建立了这种多模态认知逻辑的证明理论和kripke型模型理论。子结构逻辑的代数研究。α - 1密集集片段上的马丁公理的结果。

Among other multi-modal logics, we dealt mainly with multi-agent epistemic logics. We can describe inter-personal epistemic inference by making use of multi-agent epistemic logics, and hence we can apply them to game theory. As application, we tried mainly to analyze the game theoretical decision-making process. The idea of applying multi-modal epistemic logics enables us to get new perspectives on relations between epistemic logic and game theory. Many suggestions on future research were obtained.We found that the restriction of inter-personal epistemic inference to "shallow depths" is an important aspect of bounded rationality.In this system IGEF, we can bescribe such restriction by making use of thought sequents. Our system enables us to 'isolate' inter-personal epistemic inference from other ability, and to consider bounded rationality as restrictions on the ability of inter-personal epistemic inference. Moreover, we succeeded to construct the extended Kripke-type semantics for such multi-modal epistemic logics.The main and ralated results are the following.1. Systems IGEF of multi-agent epistemic logics with the feature of the restriction of inter-personal epistemic inference to shallow depths are constructed. These systems enable us to describe contentwise cost of inter-personal epistemic inference in game theoretical situations.2. The proof theory and Kripke-type model theory for such multi-modal epistemic logics are established.3. Algebraic study of substructural logics.4. Results on Martin's axiom on fragmnets of aleph-one dense sets.