Bull's Theorem by the Method of Diagrams

We show how to use diagrams in order to obtain straightforward completeness theorems for extensions of K4.3 and a very simple and constructive proof of Bull's theorem: every normal extension of S4.3 has the finite model property.     

内隐记忆的证明逻辑与加工分离说（PDP）的修正模型

讨论了内隐记忆的证明逻辑和内隐与外显测验中的意识和无意识影响问题。间接证明内隐记忆的逻辑应用在功能分离实验中。它的前提假设是记忆测验都是＂纯净＂的。直接证明逻辑应用在匹配比较实验中。它认为测验中的意识和无意识影响是并存的,Ｊａｃｏｂｙ等人近期提出的加工分离说（ＰＤＰ）在匹配比较法的基础上,将测验中的意识和无意识影响进行了分离,并借用经典测验理论的公式计算这两种影响。作者认为,按照概率论关于两个随机独立事件之和与积的运算法则,必须把包含测验（ｉｎｃｌｕｓｉｏｎｔｅｓｔ）的公式修正为Ｉｎｃｌｕｓｉｏｎ＝Ｒ（１－ａ）＋Ａ（１－Ｒ）。修正过的ＰＤＰ由四个方程组成。它不仅考虑了原ＰＤＰ忽视的外显条件下的无意识缺失（１－ａ）,而且可以更加确切地估计回忆概率（Ｒ）。这在数学理论上已找到了证据。     

Socratic Proofs and Paraconsistency: A Case Study

This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φ_v. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.     

A logical formalization of the OCC theory of emotions

In this paper, we provide a logical formalization of the emotion triggering process and of its relationship with mental attitudes, as described in Ortony, Clore, and Collins’s theory. We argue that modal logics are particularly adapted to represent agents’ mental attitudes and to reason about them, and use a specific modal logic that we call Logic of Emotions in order to provide logical definitions of all but two of their 22 emotions. While these definitions may be subject to debate, we show that they allow to reason about emotions and to draw interesting conclusions from the theory.     

Leibniz Filters Revisited

Leibniz filters play a prominent role in the theory of protoalgebraic logics. In [3] the problem of the definability of Leibniz filters is considered. Here we study the definability of Leibniz filters with parameters. The main result of the paper says that a protoalgebraic logic S has its strong version weakly algebraizable iff it has its Leibniz filters explicitly definable with parameters.     

A Map of Common Knowledge Logics

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole.     

Correspondence Results for Relational Proof Systems with Application to the Lambek Calculus

We present a general framework for proof systems for relational theories. We discuss principles of the construction of deduction rules and correspondences reflecting relationships between semantics of relational logics and the rules of the respective proof systems. We illustrate the methods developed in the paper with examples relevant for the Lambek calculus and some of its extensions.