Equivalents of Mingle and Positive Paradox

Relevant logic is a proper subset of classical logic. It does not include among its theorems any ofpositive paradox A (B A)mingle A (A A)linear order (A B) (B A)unrelated extremes (A ) (B B¯)This article shows that those four formulas have different effects when added to relevant logic, and then lists many formulas that have the same effect as positive paradox or mingle.     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

The Logic of Instance Ontology

An ontology's theory of ontic predication has implications for the concomitant predicate logic. Remarkable in its analytic power for both ontology and logic is the here developed Particularized Predicate Logic (PPL), the logic inherent in the realist version of the doctrine of unit or individuated predicates. PPL, as axiomatized and proven consistent below, is a three-sorted impredicative intensional logic with identity, having variables ranging over individuals x, intensions R, and instances of intensions Ri. The power of PPL is illustrated by its clarification of the self-referential nature of impredicative definitions and its distinguishing between legitimate and illegitimate forms. With a well-motivated refinement on the axiom of comprehension, PPL is, in effect, a higher-order logic without a forced stratification of predicates into types or the use of other ad hoc restrictions. The Russell–Priest characterization of the classic self-referential paradoxes is used to show how PPL diagnosis and solves these antimonies. A direct application of PPL is made to Grelling's Paradox. Also shown is how PPL can distinguish between identity and indiscernibility.     

四卡问题解决中的内容与逻辑分析效应

选取条件概率(P(Q|P))由低到高的四个命题作为四卡问题中的检验规则,探讨了大学生被试对四张卡片的逻辑证明作用的推断能力及其对解决四卡问题的影响。结果发现:(1)不同条件概率的命题之间正确选择P-Q的人数百分比不存在显著差异,命题的条件概率因素对四卡问题的正确解决没有影响。(2)逻辑分析过程对四卡问题的正确解决产生了一定的抑制作用,这可能是因为被试不能从整体上思考四张卡片在命题检验中的逻辑作用的缘故。(3)一些被试即使在逻辑分析过程中表现出知道-Q卡片的证伪作用,仍然倾向于选择卡片Q而非-Q,这一现象再次证实了人类思维的非形式逻辑的一面。     

冠脉介入治疗合理临床应用的思维基础

冠心病的发病率逐年升高,死亡率居高不下,成为威胁人类健康的重要疾病。人们为了攻克这一难题进行了不懈的工作,溶栓、监护及介入治疗的出现挽救了众多生命。随着冠状动脉介入治疗方法的不断完善和广泛开展,冠状动脉介入治疗越来越成为冠心病治疗的主要临床手段。但随之而来的手术并发症、支架在狭窄等问题成为不得不考虑的问题。治疗策略的选...     

Causes,Counterfactuals, and Non-Locality

In order to motivate the thesis that there is no single concept of causation that can do justice to all of our core intuitions concerning that concept, Ned Hall has argued that there is a conflict between a counterfactual criterion of causation and the condition of causal locality. In this paper I critically examine Hall's argument within the context of a more general discussion of the role of locality constraints in a causal conception of the world. I present two strategies that defenders of counterfactual accounts of causation can pursue to respond to Hall's challenge—including the adoption of a counterfactual condition that is sufficient for causal action-at-a-distance in place of Hall's ‘process’ condition—and conclude that Hall's argument against counterfactual accounts of causation is unsuccessful.     

“亚当·斯密问题”的逻辑张力

“亚当·斯密问题”是指斯密的《国富论》与《道德情操论》之间存在着对立或不一致的问题,最初由十九世纪中叶的德国历史学派所提出。此后,随着现实与理论的发展,出现了不同的看法。学者们普遍认为,斯密的两大著作之间、经济学与伦理学之间存在着对立或者不存在对立,而是相互一致的。这些看法都具有各自的积极合理的内容,但缺乏辩证的观点,而没有看到“斯密问题”自身的逻辑张力,也就是说,“斯密问题”所指涉的是现实的经济与伦理之间及作为其理论表现的经济学与伦理学之间的关系。“斯密问题”所含的这些关系呈现出了一个动态的、由肯定到否定再到否定之否定的辩证过程。     

Characterizing Simpler Recognizable Sets of Integers

For a given numeration system U, a set X of integers is said to be U-star-free if the language of the normalized U-representations of the elements in X is star-free. Adapting a result of McNaughton and Papert, we give a first-order logical characterization of these sets for various numeration systems including integer base systems and the Fibonacci system. For k-ary systems, the problem of the base dependence of this property is also studied. Finally, the case of k-adic systems is developed.     

Symmetric Propositions and Logical Quantifiers

Symmetric propositions over domain and signature are characterized following Zermelo, and a correlation of such propositions with logical type- quantifiers over is described. Boolean algebras of symmetric propositions over and Σ are shown to be isomorphic to algebras of logical type- quantifiers over . This last result may provide empirical support for Tarski’s claim that logical terms over fixed domain are all and only those invariant under domain permutations.