Semantics for Dual and Symmetric Combinatory Calculi

We define dual and symmetric combinatory calculi (inequational and equational ones), and prove their consistency. Then, we introduce algebraic and set theoretical– relational and operational – semantics, and prove soundness and completeness. We analyze the relationship between these logics, and argue that inequational dual logics are the best suited to model computation.     

New Intuitionistic Logical Constants and Novikov Completeness

Extending the language of the intuitionistic propositional logic Int with additional logical constants, we construct a wide family of extensions of Int with the following properties: (a) every member of this family is a maximal conservative extension of Int; (b) additional constants are independent in each of them. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Finite Model Property for the Implicational Fragment of IPC Without Exchange and Contraction

The aim of this paper is to show that the implicational fragment BKof the intuitionistic propositional calculus (IPC) without the rules of exchange and contraction has the finite model property with respect to the quasivariety of left residuation algebras (its equivalent algebraic semantics). It follows that the variety generated by all left residuation algebras is generated by the finite left residuation algebras. We also establish that BKhas the finite model property with respect to a class of structures that constitute a Kripke-style relational semantics for it. The results settle a question of Ono and Komori [OK85]. This revised version was published online in June 2006 with corrections to the Cover Date.     

儿童口语词汇获得年龄效应

获得年龄是指儿童第一次学会某个词的年龄。单词获得年龄效应是指早获得的词比晚获得的词加工快。该简要概述了获得年龄数据的收集以及获得年龄在成人词典加工中的作用,重点介绍了获得年龄效应与频率效应的关系的研究,并对获得年龄效应的机制进行了简要的评述。     

Mathematical modal logic: A view of its evolution

This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so. It focuses on the interconnections between algebraic semantics using Boolean algebras with operators and relational semantics using structures often called Kripke models. It reviews the ideas of a number of people who independently contributed to the emergence of relational semantics, and compares them with the work of Kripke. It concludes with an account of several applications of modal model theory to mathematics and theoretical computer science.     

潮汕话-普通话双言者的词汇习得年龄效应

采用潮汕话-普通话双言者为被试, 通过3个实验, 考察了词汇习得年龄效应。实验1采用汉字命名和图片命名范式, 证实了在双言者的两种语言中都存在词汇习得年龄效应。实验2和实验3分别采用语义范畴判断及声母监控任务, 在语义层面及语音层面检验了双言者的两种语言的词汇习得年龄效应的特点。结果表明, 在语义任务上发现了词汇习得年龄效应, 在语音任务上未发现。整个研究表明, 语义在汉语词汇习得年龄效应产生中具有重要作用, 支持了语义假设。     

A Completeness Proof for a Logic with an Alternative Necessity Operator

We show the completeness of a Hilbert-style system LK defined by M. Valiev involving the knowledge operator K dedicated to the reasoning with incomplete information. The completeness proof uses a variant of Makinson's canonical model construction. Furthermore we prove that the theoremhood problem for LK is co-NP-complete, using techniques similar to those used to prove that the satisfiability problem for propositional S5 is NP-complete.