Expansion and Contraction of Finite States

We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.     

Vagueness and Blurry Sets

This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S ₁ to the effect that Bob is bald is x true, for x in [0,1], there should be a further statement S ₂ which tells us how true S ₁ is, and so on – that is, it accommodates higher-order vagueness – without resorting to the claim that the metalanguage in which the semantics of vagueness is presented is itself vague, and without requiring us to abandon the idea that the logic – as opposed to the semantics – of vague discourse is classical. I model the extension of a vague predicate P as a blurry set, this being a function which assigns a degree of membership or degree function to each object o, where a degree function in turn assigns an element of [0,1] to each finite sequence of elements of [0,1]. The idea is that the assignment to the sequence 0.3,0.2, for example, represents the degree to which it is true to say that it is 0.2 true that o is P to degree 0.3. The philosophical merits of my theory are discussed in detail, and the theory is compared with other extensions and generalisations of fuzzy logic in the literature.     

A Grim Semantics For Logics of Belief

Patrick Grim has presented arguments supporting the intuition that any notion of a totality of truths is incoherent. We suggest a natural semantics for various logics of belief which reflect Grim’s intuition. The semantics is a topological semantics, and we suggest that the condition can be interpreted to reflect Grim’s intuition. Beyond this, we present a natural canonical topological model for K4 and KD4.     

人格特质与认知操作关系的初步研究

本研究采用NEO PI R测试 ,以逻辑推理为认知操作指标 ,初步考察了人格特质与大学生认知操作的关系。结果表明 :①神经质、外倾性与逻辑推理有显著负相关 ,开放性则与之呈正相关 ;②人格特质和认知操作关系的偏相关分析与相关分析的结果基本一致 ;③多元逐步回归分析显示 ,外倾性与逻辑推理有负性预测关系 ,开放性及严谨性则与逻辑推理有正性预测关系 ;④人格特质与认知操作的关系受操作难度、认知任务和兴趣类型等因素制约。     

A Simple Incomplete Extension of T which is the Union of Two Complete Modal Logics with f.m.p.

I present here a modal extension of T called KTLM which is, by several measures, the simplest modal extension of T yet presented. Its axiom uses only one sentence letter and has a modal depth of 2. Furthermore, KTLM can be realized as the logical union of two logics KM and KTL which each have the finite model property (f.m.p.), and so themselves are complete. Each of these two component logics has independent interest as well.     

科学心理学的观念与人文科学的逻辑奠基

科学心理学观念的普遍兴起,是19世纪中叶错综复杂的思想史背景的产物。只有在人类思想及其历史作为整体的关系背景中,才能澄清这个观念的内在本性。也只有在系统地接受这个背景的制约关系中,这个观念才能获得其真理的实现。能否在人类思想作为整体中胜任并执行其理论职能,成为我们检验一种心理学体系之真理性的途径之一:科学心理学观念只有实现为现象学心理学,才能执行其为人文科学奠基的逻辑职能; 反之亦然。这个关系还从否定方面暗示着,一切以异化的形式实现的心理学,都不可能真正承担起为人文科学奠基的逻辑职能,并因而违背了我们的常识。     

Fragments of R-Mingle

The logic RM and its basic fragments (always with implication) are considered here as entire consequence relations, rather than as sets of theorems. A new observation made here is that the disjunction of RM is definable in terms of its other positive propositional connectives, unlike that of R. The basic fragments of RM therefore fall naturally into two classes, according to whether disjunction is or is not definable. In the equivalent quasivariety semantics of these fragments, which consist of subreducts of Sugihara algebras, this corresponds to a distinction between strong and weak congruence properties. The distinction is explored here. A result of Avron is used to provide a local deduction-detachment theorem for the fragments without disjunction. Together with results of Sobociski, Parks and Meyer (which concern theorems only), this leads to axiomatizations of these entire fragments — not merely their theorems. These axiomatizations then form the basis of a proof that all of the basic fragments of RM with implication are finitely axiomatized consequence relations.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

Synonymous Logics

This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are synonymous or translationally equivalent. We discuss a proposed formal definition of translational equivalence, show why it is reasonable, and also discuss its relation to earlier definitions in the literature. We also give a simple criterion for showing that two modal logics are not translationally equivalent, and apply this to well-known examples. Some philosophical morals are drawn concerning the possibility of having two logical systems that are empirically distinct but are both translationally equivalent to a common logic.     

Game Logic is Strong Enough for Parity Games

We investigate the expressive power of Parikh's Game Logic interpreted in Kripke structures, and show that the syntactical alternation hierarchy of this logic is strict. This is done by encoding the winning condition for parity games of rank n. It follows that Game Logic is not captured by any finite level of the modal -calculus alternation hierarchy. Moreover, we can conclude that model checking for the -calculus is efficiently solvable iff this is possible for Game Logic