论逻辑语义

符号、由符号构成的某类表达式及其语义是语言哲学和符号哲学研究的一个重要方面 ,逻辑符号、由逻辑符号构成的某类表达式及其逻辑语义则是逻辑哲学研究的一个重要方面。逻辑 ,特别是现代逻辑 ,通常是用形式语言和形式系统表述的。但逻辑学家建立逻辑的目的是为了刻画人的思维规律和推理能力 ,这必然要涉及形式语义和形式系统的逻辑语义。逻辑语义可以分为两大类 :直观语义和形式语义。很少有论文专门论述逻辑语义中的直观语义以及它们与形式语义的关系。本文主要讨论这些问题。给定一个形式语言L。我们知道 ,从本质上说 ,L由一堆抽象符号…     

停下即完成:“知道如何”的弱逻辑（英文）

本论文针对王彦晶提出的"知道如何"的模态算子提出了一种新的语义。与原来的语义相比,我们的语义比较弱但是却更容易实现。根据该语义,主体知道如何从状态到达状态?当且仅当主体有一个有穷的线性动作系列使得执行该动作系列停止后的状态即是目的状态。这种弱化的新语义导致了一种弱化的逻辑。原来逻辑系统里面的组合公理在我们的新语义下不再有效。我们也给出了该逻辑的一个公理系统并证明了其可靠性和完全性。同时,我们也证明了该逻辑具有可判定性。     

刻画主体有智能的逻辑(英文)

本文提出两个标准来表示"一个主体有智能":该主体知道它的知识和它做过的活动。然后我们给出若干逻辑系统分别整体地、局部地和半局部地刻画上述标准。最后我们证明这些系统相对各自的语义是框架可靠和框架完全的。     

中国古代逻辑方法论的源头——《周易》逻辑方法论探析

《周易》的卦爻符号系统及其语义说明,已经使用了一定的逻辑方法．建立在阴阳两爻这种初始语言上的符号系统,有一套自定的格式语言和规则．《周易》中的其他逻辑方法,如关于“象”的方法,关于“辞”的方法,关于“取象比类”的方法,都有其正确、合理的方面,但也都有随意性的缺憾．这些逻辑方法,奠定了中国传统思维模式的源头基础,应当成为中国古代逻辑思想史研究领域的一个课题．     

早期分析哲学中的信念逻辑

弗雷格的涵义/意谓理论为信念句子的句法和语义分析提供了一个框架。一个信念句子由专名、动词"相信"和从句组成。根据弗雷格的从句理论,从句有间接意谓,即它的思想。按弗雷格的分析,可以建立信念逻辑的形式语言和语义。这种语义是混合式的,引入涵义、个体和真值三类本体。还可以建立一个弗雷格式的信念逻辑系统。它是不需要可能世界语义学的信念逻辑。罗素先后提出处理信念语境中同一替换律失效问题的摹状词理论、信念关系论和逻辑原子主义。但罗素没有对信念句子的句法和语义作出明确的分析。     

索引语词的逻辑研究

所谓索引语词就是指在不知其使用语境时,便无从确定其所指语义的一个词或表达式。对索引语词来说,首先必须知道是谁正在说或者写它,并且是在何时,何处说和写它,以便知道它所指的具体事物是什么。比如,所有的人称代词都是索引词,因为要知道“你”或“我”指的是谁,我们就必须知道谁正在说谁或者写谁。“昨天”、“今天”和“明天”以及所有的时态动词也是索引语词,因为它们的时间指称是语境的一个函项。 索引语词的逻辑研究主要是在逻辑语用学的     

将证成逻辑里的加号解释为证成集的联集（英文）

在证成逻辑的研究中,加号所扮演的角色总是需要特别加以说明。在这篇文章中我们将厘清加号的功能,并提出一个新的证成逻辑系统,在此系统中加号将被解释为较符合直觉的证成集的联集。我们将提供该系统的语义并证明其完备性,然后建立此一新系统与传统证成逻辑之间关係,并由此关傺证明新系统也具有"实现理论"。最后我们将讨论这个新的证成逻辑的算术语义。     

含例邻域逻辑的萨奎斯特对应理论（英文）

本文给出含例邻域逻辑的萨奎斯特对应理论。这种逻辑可以讨论一个可能世界的邻域的存在性信息,是关系语义和邻域语义的一种混合。增加的表达力和描述邻域函数的关系特征使我们可以在框架层面讨论这种语言可以定义什么性质,是否可以超越邻域语义的KW片段。我们给出对应定理的两个证明。第一个证明直接使用标准翻译和极小赋值的技术,第二个证明通过双模态翻译将含例邻域逻辑的对应问题转化为经典克里普克语义的双模态逻辑。     

关于函数依赖关系的认知逻辑（英文）

对非经典知识,尤其是"知道是什么"的研究几乎是与对经典的认知逻辑的研究同时开始的,并且近来此类研究又吸引了诸多学者的注意。此种"知道是什么"算子能用来表达认知主体对个别变量的值的知识,但仅靠其自身却无法表达主体对变量之间的关系的知识。本文尝试提出一种算子来表达主体对变量间的函数关系的知识。不同于相关研究中类似的用于表达函数依赖关系的其它算子,这种算子的语义引入了一个先验函数域,用以表达认知主体对函数依赖关系的先验可能性的限制。我们将讨论该种语义下由不同的先验函数域引出的三种单主体逻辑,然后将其统一到一个逻辑当中并扩充为多主体逻辑。     

一类命题逻辑的一般弱框架择类语义

命题逻辑的一般弱框架择类语义是相干邻域语义的变形,其特点是：采用择类运算来刻画逻辑常项;语义运算与逻辑联结词之间有清晰的对应关系,可以从整体上处理一类逻辑,具有普适性。本文将这种语义用于一类B、C、K、W命题逻辑,包括相干逻辑R及其线性片段、直觉主义逻辑及其BCK片段等,并借助典范框架和典范赋值,证明了这些逻辑系统的可靠性和完全性。     

Abstract Valuation Semantics

We define and study abstract valuation semantics for logics, an algebraically well-behaved version of valuation semantics. Then, in the context of the behavioral approach to the algebraization of logics, we show, by means of meaningful bridge theorems and application examples, that abstract valuations are suited to play a role similar to the one played by logical matrices in the traditional approach to algebraization.     

Logics for Epistemic Programs

We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dynamic logic, and indeed our languages are not significantly more complicated than dynamic logics. But the semantics is more complicated. In general, the semantics of an epistemic program is what we call aprogram model. This is a Kripke model of ‘actions’,representing the agents' uncertainty about the current action in a similar way that Kripke models of ‘states’ are commonly used in epistemic logic to represent the agents' uncertainty about the current state of the system. Program models induce changes affecting agents' information, which we represent as changes of the state model, called epistemic updates. Formally, an update consists of two operations: the first is called the update map, and it takes every state model to another state model, called the updated model; the second gives, for each input state model, a transition relation between the states of that model and the states of the updated model. Each variety of epistemic actions, such as public announcements or completely private announcements to groups, gives what we call an action signature, and then each family of action signatures gives a logical language. The construction of these languages is the main topic of this paper. We also mention the systems that capture the valid sentences of our logics. But we defer to a separate paper the completeness proof. The basic operation used in the semantics is called the update product. A version of this was introduced in Baltag et al. (1998), and the presentation here improves on the earlier one. The update product is used to obtain from any program model the corresponding epistemic update, thus allowing us to compute changes of information or belief. This point is of interest independently of our logical languages. We illustrate the update product and our logical languages with many examples throughout the paper.     

Convex MV-Algebras: Many-Valued Logics Meet Decision Theory

This paper introduces a logical analysis of convex combinations within the framework of ?ukasiewicz real-valued logic. This provides a natural link between the fields of many-valued logics and decision theory under uncertainty, where the notion of convexity plays a central role. We set out to explore such a link by defining convex operators on MV-algebras, which are the equivalent algebraic semantics of ?ukasiewicz logic. This gives us a formal language to reason about the expected value of bounded random variables. As an illustration of the applicability of our framework we present a logical version of the Anscombe–Aumann representation result.     

Action negation and alternative reductions for dynamic deontic logics

Dynamic deontic logics reduce normative assertions about explicit complex actions to standard dynamic logic assertions about the relation between complex actions and violation conditions. We address two general, but related problems in this field. The first is to find a formalization of the notion of ‘action negation’ that (1) has an intuitive interpretation as an action forming combinator and (2) does not impose restrictions on the use of other relevant action combinators such as sequence and iteration, and (3) has a meaningful interpretation in the normative context. The second problem we address concerns the reduction from deontic assertions to dynamic logic assertions. Our first point is that we want this reduction to obey the free-choice semantics for norms. For ought-to-be deontic logics it is generally accepted that the free-choice semantics is counter-intuitive. But for dynamic deontic logics we actually consider it a viable, if not, the better alternative. Our second concern with the reduction is that we want it to be more liberal than the ones that were proposed before in the literature. For instance, Meyer's reduction does not leave room for action whose normative status is neither permitted nor forbidden. We test the logics we define in this paper against a set of minimal logic requirements.     

Process and Action: Relevant Theory and Logics

Whileprocess andaction are fundamental notions, in ubiquitous use, they lack satisfactory logical treatment in two critical respects: in analyses of the fundamentals themselves and in logical development. For what treatment they have so far received, under classical systematisation, leaves significant lacunae and induces much paradox. A relevant logical relocation, carried through in detail here, removes such problems, and provides solid ground-work for a satisfactory treatment.Firstly, as to fundamentals: processes should be explicated, so it is argued, as certain sorts of (time) directed functions (from inputs to outputs); thus they can be represented through certain ordered pairs of relations. Significant logical structures they can enter into are investigated: notably, process lattice and coupled logics, and a generalized category theory (tolerating nonassociativity of composition).Actions are types of processes, agent-ascribed process. As stock analyses of the differentia, operators and agency, through intentionality, rationality and so on, demonstrably fail, new causal analyses are proposed.Secondly, as to logical developments: for the most part, the apparently diverse offering of process and action logics to be encountered in the literature are but multiple modal logics: modal logics enriched with further functors of interesting modal sorts. Some, for example, like advertised process logics are dynamic logics (themselves basically multiple modal logics) enriched by tense logical functors, themselves modal in character. In a way that is now becoming nonstandardly standard, these modal enterprises can be reworked on relevant logical bases. A main point to such exercises resembles that of other relevant reworkings: namely, the search for correctness, for adequacy to pre-analytic and linguistic data, and therewith removal of paradoxes and anomalies that accumulate under modal analyses.Logical components from a properly expanded Humean model of action are supplied with relevant logics and semantics, in particulardoing, trying andstriving, intention andmotivation. The difficult question of formalising practical inference is then addressed.Relevant dynamic logics, paralleling modal developments, are built up piece by piece, relevant theory change is considered within a dynamic framework, and work on relevant temporal and process logics of programming cast, including functors such asbefore, during andthroughout, is initiated. The present state of logical play is assessed.I have been much encouraged in this work by Krister Segerberg, who deserves and has my considerable thanks. It will be evident that his fine investigative work, which I want to seefurthered, has served as a foil in much of what follows.     

Logics of public communications

Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. This paper was originally published as Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z.W. Ras (Eds.), Proceedings of the fourth international symposium on methodologies for intelligent systems: Poster session program (pp. 201–216). Publisher: Oak Ridge National Laboratory, ORNL/DSRD-24. Research partly supported by NSF Grant CCR-8702307 and PSC-CUNY Grant 668283.     

Grafting Modalities onto Substructural Implication Systems

We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first two authors in a previous paper.     

Combinations of Tense and Modality for Predicate Logic

In recent years combinations of tense and modality have moved into the focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of predicate logic are desirable, and in this paper I present two such results. The main developments in this area can be split into two directions, differing in the question whether the ordering of time is world-independent or not. Semantically, this difference appears in the discussion whether T×W-frames or Kamp-frames (resp. Ockham-frames) provide a suitable semantics for combinations of tense and modality. Here, two calculi are presented, the first adequate with respect to Kamp-semantics, the second to T×W-semantics. (Both calculi contain an appropriate version of Gabbay's irreflexivity rule.) Furthermore, the proposed constructions of canonical frames simplify some of those which have hitherto been discussed.     

Definability and Interpolation in Non-Classical Logics

Algebraic approach to study of classical and non-classical logical calculi was developed and systematically presented by Helena Rasiowa in [48], [47]. It is very fruitful in investigation of non-classical logics because it makes possible to study large families of logics in an uniform way. In such research one can replace logics with suitable classes of algebras and apply powerful machinery of universal algebra. In this paper we present an overview of results on interpolation and definability in modal and positive logics,and also in extensions of Johansson's minimal logic. All these logics are strongly complete under algebraic semantics. It allows to combine syntactic methods with studying varieties of algebras and to flnd algebraic equivalents for interpolation and related properties. Moreover, we give exhaustive solution to interpolation and some related problems for many families of propositional logics and calculi. This paper is a version of the invited talk given by the author at the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005. Presented by Jacek Malinowski