Actuality in Propositional Modal Logic

We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula ${\phi}$ in the propositional modal language with A, there is a formula ${\psi}$ not containing A such that ${\phi}$ and ${\psi}$ are materially equivalent at the actual world in every Kripke model (respectively, neighborhood model). Inspection of the proofs leads to corresponding proof-theoretic results concerning the eliminability of the actuality operator in the actuality extension of any normal propositional modal logic and of any “classical” modal logic. As an application, we provide an alternative proof of a result of Williamson’s to the effect that the compound operator A□ behaves, in any normal logic between T and S5, like the simple necessity operator □ in S5.     

The Logic of Theory Assessment

This paper starts by indicating the analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper consists in working out the claim that one can have Hempel’s cake and eat it too — in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, α is an acceptable theory for evidence β if and only if α is both sufficiently plausible given β and sufficiently informative about β. This is spelt out in terms of ranking functions (Spohn, 1988) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, 2000) as well as to nonmonotonic consequence relations (Kraus et al., 1990). It concludes by relating the plausibility-informativeness approach to Carnap’s positive relevance account, thereby shedding new light on Carnap’s analysis as well as solving another problem of confirmation theory. A precursor of this paper has appeared as “The Logic of Confirmation and Theory Assessment” in L. Běhounek & M. Bílková (eds.), The Logica Yearbook 2004, Prague: Filosofia, 2005, 161–176.     

马克思分配公正思想的逻辑生成 ——基于《哥达纲领批判》视阈

马克思关于生产方式决定分配方式的历史唯物主义观点是认知和建构分配公正的逻辑前提。在共产主义社会第一阶段,要以创造价值的劳动为基本尺度实行分配,即按劳分配,虽然以劳动为尺度对社会总产品进行分配的原则超越了"按资分配",但按劳分配也是特殊公正论,仍然是形式公正,是初步的、非完全意义上的实质公正。分配的实质公正——按需分配,只有在共产主义社会高级阶段才能实现。     

The Logic of Plausible Reasoning: A Core Theory

The paper presents a core theory of human plausible reasoning based on analysis of people's answers to everyday questions about the world. The theory consists of three parts:

• 1 a formal representation of plausible inference patterns; such as deductions, inductions, and analogies, that are frequently employed in answering everyday questions;
• 2 a set of parameters, such as conditional likelihood, typicality, and similarity, that affect the certainty of people's answers to such questions; and
• 3 a system relating the different plausible inference patterns and the different certainty parameters.

This is one of the first attempts to construct a formal theory that addresses both the semantic and parametric aspects of the kind of everyday reasoning that pervades. all of human discourse.     

Proof Theory of Paraconsistent Quantum Logic

Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type sequent calculi for these logics and their close relatives is addressed.     

Proof Theory for Functional Modal Logic

We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \(\mathord {\sim }\mathord {\Box }A\equiv \mathord {\Box }\mathord {\sim }A\). We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.     

Stoic Sequent Logic and Proof Theory

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness.     

Logic and the Classical Theory of Mind

I extract several common assumptions in the Classical Theory of Mind (CTM) – mainly of Locke and Descartes – and work out a partial formalisation of the logic implicit in CTM. I then define the modal (logical) properties and relations of propositions, including the modality of conditional propositions and the validity of argument, according to the principles of CTM: that is, in terms of clear and distinct ideas, and without any reference to either possible worlds, or deducibility in an axiomatic system, or linguistic convention.     

佛学情论及其内在理路探析

佛学情论思想系统而深刻,涵盖了情的生成论、情的类型论以及情的解脱论。在情的生成方面,佛学认为人类的情绪和情感是缘起而在的,是环境、生理、认知和行为等主观、客观条件因缘和合的产物;在情的类型方面,佛学以贪、嗔、痴为基点,对消极情绪和情感进行了系统探讨,并关注了忿、恨、恼、疑、嫉等消极情绪和情感,为了对治消极情绪和情感,佛学还深入探讨了无贪、无嗔、无痴以及惭愧和四无量心等积极情绪与情感;在情的解脱方面,佛学以三法印为理论基础,以四谛为理论框架,以中道行为基本原则,以"戒、定、慧"三学为修行法门,以期用佛法的智慧化解消极情绪和情感,涵育积极情绪和情感。     

Asymptotic Densities in Logic and Type Theory

This paper presents a systematic approach for obtaining results from the area of quantitative investigations in logic and type theory. We investigate the proportion between tautologies (inhabited types) of a given length n against the number of all formulas (types) of length n. We investigate an asymptotic behavior of this fraction. Furthermore, we characterize the relation between number of premises of implicational formula (type) and the asymptotic probability of finding such formula among the all ones. We also deal with a distribution of these asymptotic probabilities. Using the same approach we also prove that the probability that randomly chosen fourth order type (or type of the order not greater than 4), which admits decidable lambda definability problem, is zero. Presented by Jacek Malinowski     

Logic and Ontology in Hegel's Theory of Predication

In this paper I sketch some arguments that underlie Hegel's chapter on judgment, and I attempt to place them within a broad tradition in the history of logic. Focusing on his analysis of simple predicative assertions or ‘positive judgments’, I first argue that Hegel supplies an instructive alternative to the classical technique of existential quantification. The main advantage of his theory lies in his treatment of the ontological implications of judgments, implications that are inadequately captured by quantification. The second concern of this paper is the manner in which Hegel makes logic not only dependent on ontology generally, but also variant in regard to domains of objects. In other words, he offers a domain‐specific logical theory, according to which the form of judgment or inference is specific to the subject of judgment. My third concern lies with the metaphilosophical consequences of this theory, and this includes some more familiar Hegelian themes. It is well known that Hegel frequently questioned the adequacy of the sentential form for expressing higher order truths. My reading of his theory of predication explains and contextualizes this tendency by demystifying notions like the so‐called speculative proposition.     

The Place of Dialogue Theory in Logic,Computer Science and Communication Studies

Dialogue theory, although it has ancient roots, was put forward in the 1970s in logic as astructure that can be useful for helping to evaluate argumentation and informal fallacies.Recently, however, it has been taken up as a broader subject of investigation in computerscience. This paper surveys both the historical and philosophical background of dialoguetheory and the latest research initiatives on dialogue theory in computer science. The main components of dialogue theory are briefly explained. Included is a classification of the main types of dialogue that, it is argued, should provide the central focus for studying many important dialogue contexts in specific cases. Following these three surveys, a concluding prediction is made about the direction dialogue theory is likely to take in the next century, especially in relation to the growing field of communication studies.     

论马克思市民社会理论的两种逻辑

<正>人们近年来围绕着马克思的市民社会理论进行了很多研究,不过,在笔者看来,这些研究尚未完全阐明这一理论的所有基本问题,因而对其作进一步研究的空间仍是敞开的。一个直接的问题是:人     

服务型政府建设:理论范式与实践逻辑

服务型政府作为一种基于公民本位、崇尚服务理念、追求公共利益的现代政府模式,近年来逐渐成为我国政府改革中的热门话语。服务型政府的建设是一个综合性课题,在委托代理理论、新公共管理、新公共服务和公共治理理论的基石上,为了更好地实现公正与平等、效率与竞争、廉洁与透明、民主与参与等公共价值,建设法治政府、有限政府、责任政府、回应型政府和企业型政府成了必然的路径选择,这亦是实现善治的必然逻辑。     

黑格尔实践哲学的现实性

本文对黑格尔实践哲学的当代意义的众多层次进行了讨论。通过将黑格尔实践哲学与自由主义、社群主义以及其他相关社会理论进行比较分析,集中论述了三个命题,它们分别是(Ⅰ)黑格尔向我们展示了一种社会异化理论,或者更确切的说,是一种并不简单放弃"实践哲学"作为规范科学主张的"完全异化"理论;(Ⅱ)在一个包含基本法所有"生成层面"的统一的法的概念中,黑格尔区别了这一统一概念的不同层次——就如同她们最近被称之的那样。同时,将他们历史实现的问题主题化;(Ⅲ)黑格尔的法哲学包含一个政治的概念,这个概念对于现在追问国家任务的现实问题具有重大的批判意义。     

Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization

Proof-theoretical notions and techniques, developed on the basis of sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, which is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. The translation enables us to formalize and analyze free ride in terms of proof theory. The notion of normal form of Euler diagrammatic proofs is investigated, and a normalization theorem is proved. Some consequences of the theorem are further discussed: in particular, an analysis of the structure of normal diagrammatic proofs; a diagrammatic counterpart of the usual subformula property; and a characterization of diagrammatic proofs compared with natural deduction proofs.     

Braine心理逻辑理论述评

该文对Braine提出的在推理心理学研究领域占居重要地位的“心理逻辑理论”做了综合述评。“心理逻辑理论”主要包括三方面内容:构成“心理逻辑理论”基础的一组推理规则图式、将推理规则图式应用于推理过程的推理方案、实际应用意义。Braine认为他和他的同事于1984年设计并实施的以“自然推理系统”所含各推理规则为实验材料的实验结果支持该理论的基本观点。