涵义语义与关于概称句推理的词项逻辑

概称句推理具有以词项为单位的特征并且词项的涵义在其中起到了重要的作用。已有的处理用A一表达式表达涵义,不够简洁和自然。亚里斯多德三段论是一种词项逻辑,但它是外延的和单调的。这两方面的情况使得有必要考虑新的词项逻辑。涵义语义的基本观点是：语词首先表达的是涵义,通过涵义的作用,语词有了指称,表达概念。概称句三段论是更为常用的推理,有两个基本形式GAG和Gaa。在涵义语义的基础上建立的系统GAG和Gaa是关于这两种推理的公理系统。     

概称句词项逻辑系统GAG与Gaa的完全性

GAG与Gaa是关于概称句推理的逻辑系统。概称句词项逻辑的要点是引入了表示概念的词项,从而以更自然的方式表示概念在推理中的作用,这也带来了概称句词项逻辑语言的特点。涵义语义是用于概称句词项逻辑语言的形式语义。在涵义语义下GAG与Gaa是可靠的,但是完全性证明一直空缺。通过完全性证明,发现有必要对原来的涵义语义做一些补充和完善,为此提出涵义语义结构的一般形式,进而给出全涵义结构和实涵义结构。原来的语义结构实际上是全涵义结构。完全性证明需要使用实涵义结构。实涵义结构的框架部分与解释函数有关,因而不完全独立于被解释的语言。实涵义结构更像是认知主义语义观下的语义构造。长期以来,实在论语义观在逻辑学研究中根深蒂固。实涵义结构的提出,对这类逻辑研究的哲学基础提出了反思。     

概称句推理与排序

概称句推理可分为主要通过演绎方式的和主要通过归纳方式的。对于演绎方式进行的推理又可根据研究关注点的不同分为结论是事实句的推理和结论是概称旬的推理。由于概称句的作用,这三种类型的推理都是非单调推理。通过分别的考察,本文指出,这三种类型的概称句推理要想真正得以刻画,都需要引入前提集的排序的概念。进而,排序将是融合这三种类型推理的纽带。     

概称句的语义解释及形式化比较研究

概称句的研究始于20世纪70年代,由于概称句在思维和语言中不可或缺的地位,语言学、逻辑学、人工智能、哲学、心理学等多个领域的研究者分别从不同角度对概称句进行研究,时至今日已经提出了多种理论和形式处理方法。尽管研究视角、方法不同,对概称句进行语义分析都是研究的必经之路。本文从逻辑学研究视角,以概称句的特点为依据,将部分概称句语义研究的成果做总结和梳理,力图抓住各研究方向的思想本质,并通过论证指出周北海及毛翊[1]比较透彻地分析了概称句语义,抓住了概称句的本质。一概称句特点概述概称句(genericsentences)大体上指不表示…     

排除式CP定律的形式刻画

本文关注近年来在科学哲学等领域引起广泛关注和争议的CP定律的形式刻画。论文首先考察了CP定律的不同分类和用法,继而锁定排除式CP定律作为重点研究对象。论文对完成者方法、不变性和稳定性理论、趋向性理论和正常性解释进行了探究,同时,作为一种尝试,将逻辑学领域中对概称句的正常刻画引入CP定律的刻画之中,文末对刻画标准及这些方向进行了进一步的分析和比较。     

用概率方法解释概称句——亚里尔·科恩的概称句语义研究

用概率方法解释概称句,是概称句语义分析的一个方向。亚里尔·科恩(Ariel Cohen)[1]是近年来以概率视角对概称句进行分析研究的一位有代表性的学者,本文介绍亚里尔·科恩对概称句的解释,并以《概称句的语义解释及形式化比较研究》[2]一文中对概称句特点的讨论为依据,对科恩的解     

通过演绎方式得概称句推理的逻辑

基于[4]中的逻辑系统G,本文通过删减和增加公理及规则给出3个逻辑G0,GD和Gs,同时,我们通过对正常主项选择函数添加不同的条件给出与三个逻辑相应的不同的模型定义。其中,G0是GD和Gs的基础。这些逻辑的给出是为了刻画通过演绎方式得概称句的推理的局部推理。     

一个关于专名指称存在预设的形式刻画

目前关于预设的真值语义学研究主要是各种三值语义。这看起来有自然的一面,但其实有一个严重的误区,将"无定义"也看成一个与预设原句真值处于同一层面的真值,混淆了对象语言与元语言的区分。预设句与原句是不同层次的句子。本文试以专名指称存在预设为例,通过部分模型以及在此之上的同底扩张模型方法构造了复合模型,给出了一个既保证不同语言层次的区分又可以跨层次统一谈论原句和预设句关系的形式语义。通过这个语义,揭示了预设句与原句的2//[2]+[0]式的真值结构,使得通常情况下关于预设的默认得到形式上的刻画和呈现。     

因果影响与函数式依赖:从逻辑的视角分析

近年来,关于如何刻画系统中变量间的相互依赖和相互影响在计算机以及哲学研究中激起了广泛讨论。其中非常经典的工作包括Pearl、Gales以及Halpern等逻辑学家和计算机科学家提出的因果模型和基于因果模型的因果逻辑。而最新Baltag与van Benthem的工作又提出了通过函数式依赖这一概念分析变量间影响的模型。本文将介绍并探讨这两种路径之间的关系,并且提出,在对Halpern等人的因果模型和逻辑做认知方面的扩充之后,我们能在这两种路径中找到更多共通之处。     

STIT逻辑的发展与应用

STIT逻辑是以模态逻辑为工具来研究主事性的逻辑分支。除主事性的形式刻画以及系统构建外,STIT逻辑还研究了其他很多与主事性相关的问题,例如繁忙选择者问题、如何刻画"不做"以及主事性如何体现在言语行为或者道义语句的刻画中,等等。本文在简述STIT逻辑对主事性的不同刻画方法的基础上,分别说明了STIT逻辑对上述问题的分析和刻画。     

Gts and interrogative tableaux

A variant of the standard deductive tableau system is introduced, and interrogative rules are added, resulting in a so-called interrogative tableau system. A game-theoretical account of entailment is sketched, and the deductive tableau system is interpreted in these terms. Finally, it is shown how to extend this account of entailment into an account of interrogative entailment, thereby providing a semantics for the interrogative tableau system.     

组合原则

组合原则是逻辑语义学的基本原则,表现为函项的思想和句法与语义的对应。就构造逻辑系统而言,组合原则是一种方法论。作为延伸到自然语言形式语义学的产物,组合原则起到一种核心灵魂的作用。组合原则在理论层面和应用领域皆获得一些有价值的结果。自然语言违反组合原则的实例主要表现为歧义现象、语用因素和句法与语义不对应的情况,这正是调整组合原则的适用条件从而促进形式语义学发展的契机。     

A Sound and Complete Tableau Calculus for Reasoning about only Knowing and Knowing at Most

We define a tableau calculus for the logic of only knowing and knowing at most ON, which is an extension of Levesque's logic of only knowing O. The method is based on the possible-world semantics of the logic ON, and can be considered as an extension of known tableau calculi for modal logic K45. From the technical viewpoint, the main features of such an extension are the explicit representation of "unreachable" worlds in the tableau, and an additional branch closure condition implementing the property that each world must be either reachable or unreachable. The calculus allows for establishing the computational complexity of reasoning about only knowing and knowing at most. Moreover, we prove that the method matches the worst-case complexity lower bound of the satisfiability problem for both ON and O. With respect to [22], in which the tableau calculus was originally presented, in this paper we both provide a formal proof of soundness and completeness of the calculus, and prove the complexity results for the logic ON.     

Four semantic layers of common nouns

This article proposes a four-layer semantic structure for common nouns. Each layer matches up with a semantic entity of a certain type in Montague’s intensional semantics. It is argued that a common noun denotes a sense and a concept, which are functions. For any given context, the sense of a term determines its extensions and the concept denoted by the term specifies its intensions. Intensions are treated as sets of senses. The membership relation between a sense and an intension is a soft kind and is expressed in the form of a generic sentence. Such a layered structure explains various “degrees of publicity” of a language. The result we present clarifies the confusions existing in the ordinary understanding of “sense,” “intension,” and “concept.” It also has promising applications in interpreting metaphors and revealing the relationship between generics and metaphors.     

Free Semantics

Free Semantics is based on normalized natural deduction for the weak relevant logic DW and its near neighbours. This is motivated by the fact that in the determination of validity in truth-functional semantics, natural deduction is normally used. Due to normalization, the logic is decidable and hence the semantics can also be used to construct counter-models for invalid formulae. The logic DW is motivated as an entailment logic just weaker than the logic MC of meaning containment. DW is the logic focussed upon, but the results extend to MC. The semantics is called ‘free semantics’ since it is disjunctively and existentially free in that no disjunctive or existential witnesses are produced, unlike in truth-functional semantics. Such ‘witnesses’ are only assumed in generality and are not necessarily actual. The paper sets up the free semantics in a truth-functional style and gives a natural deduction interpetation of the meta-logical connectives. We then set out a familiar tableau-style system, but based on natural deduction proof rather than truth-functional semantics. A proof of soundness and completeness is given for a reductio system, which is a transform of the tableau system. The reductio system has positive and negative rules in place of the elimination and introduction rules of Brady’s normalized natural deduction system for DW. The elimination-introduction turning points become closures of threads of proof, which are at the points of contradiction for the reductio system.     

Some Notes on Boolos’ Semantics: Genesis,Ontological Quests and Model-Theoretic Equivalence to Standard Semantics

The main aim of this work is to evaluate whether Boolos’ semantics for second-order languages is model-theoretically equivalent to standard model-theoretic semantics. Such an equivalence result is, actually, directly proved in the “Appendix”. I argue that Boolos’ intent in developing such a semantics is not to avoid set-theoretic notions in favor of pluralities. It is, rather, to prevent that predicates, in the sense of functions, refer to classes of classes. Boolos’ formal semantics differs from a semantics of pluralities for Boolos’ plural reading of second-order quantifiers, for the notion of plurality is much more general, not only of that set, but also of class. In fact, by showing that a plurality is equivalent to sub-sets of a power set, the notion of plurality comes to suffer a loss of generality. Despite of this equivalence result, I maintain that Boolos’ formal semantics does not committ (directly) second-order languages (theories) to second-order entities (and to set theory), contrary to standard semantics. Further, such an equivalence result provides a rationale for many criticisms to Boolos’ formal semantics, in particular those by Resnik and Parsons against its alleged ontological innocence and on its Platonistic presupposition. The key set-theoretic notion involved in the equivalence proof is that of many-valued function. But, first, I will provide a clarification of the philosophical context and theoretical grounds of the genesis of Boolos’ formal semantics.     

Children's Developing Intuitions About the Truth Conditions and Implications of Novel Generics Versus Quantified Statements

Generic statements express generalizations about categories and present a unique semantic profile that is distinct from quantified statements. This paper reports two studies examining the development of children's intuitions about the semantics of generics and how they differ from statements quantified by all, most, and some. Results reveal that, like adults, preschoolers (a) recognize that generics have flexible truth conditions and are capable of representing a wide range of prevalence levels; and (b) interpret novel generics as having near‐universal prevalence implications. Results further show that by age 4, children are beginning to differentiate the meaning of generics and quantified statements; however, even 7‐ to 11‐year‐olds are not adultlike in their intuitions about the meaning of most‐quantified statements. Overall, these studies suggest that by preschool, children interpret generics in much the same way that adults do; however, mastery of the semantics of quantified statements follows a more protracted course.