AN INTUITIONISTIC CHARACTERIZATION OF CLASSICAL LOGIC

By introducing the intensional mappings and their properties, we establish a new semantical approach of characterizing intermediate logics. First prove that this new approach provides a general method of characterizing and comparing logics without changing the semantical interpretation of implication connective. Then show that it is adequate to characterize all Kripke_complete intermediate logics by showing that each of these logics is sound and complete with respect to its (unique) ‘weakest characterization property’ of intensional mappings. In particular, we show that classical logic has the weakest characterization property , which is the strongest among all possible weakest characterization properties of intermediate logics. Finally, it follows from this result that a translation is an embedding of classical logic into intuitionistic logic, iff. its semantical counterpart has the property .      

De Finetti’s No-Dutch-Book Criterion for Gödel logic

We extend de Finetti’s No-Dutch-Book Criterion to Gödel infinite-valued propositional logic.     

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     

Game Logic - An Overview

Game Logic is a modal logic which extends Propositional Dynamic Logic by generalising its semantics and adding a new operator to the language. The logic can be used to reason about determined 2-player games. We present an overview of meta-theoretic results regarding this logic, also covering the algebraic version of the logic known as Game Algebra.     

Frege and propositional unity

This paper identifies a tension in Frege’s philosophy and offers a diagnosis of its origins. Frege’s Context Principle can be used to dissolve the problem of propositional unity. However, Frege’s official response to the problem does not invoke the Context Principle, but the distinction between ‘saturated’ and ‘unsaturated’ propositional constituents. I argue that such a response involves assumptions that clash with the Context Principle. I suggest, however, that this tension is not generated by deep-seated philosophical commitments, but by Frege’s occasional attempt to take a dubious shortcut in the justification of his conception of propositional structure.     

物体的空间关系对语义相关判断的影响

采取快速语义判断任务探讨物体空间关系对语义相关判断的影响。实验1考察词对呈现方式与其指称物空间次序经验的关系对语义相关判断的影响。结果表明,词对呈现位置与其指称物的一般空间次序经验一致时语义判断快。实验2探讨词对呈现方式与其指称物构成方式的关系对语义相关判断的影响。结果表明,词对呈现方式与其指称物的构成方式一致时语义判断快。研究结果支持了知觉符号理论。     

A Davidsonian Reconciliation of Internalism, Objectivity, and the Belief-desire Theory

This paper argues that Donald Davidson's account ofassertions of evaluative judgments contains ahere-to-fore unappreciated strategy forreconciling the meta-ethical ``inconsistenttriad.' The inconsistency is thought to resultbecause within the framework of thebelief-desire theory assertions of moraljudgments must have conceptual connections withboth desires and beliefs. The connection withdesires is necessary to account for theinternal connection between such judgments andmotivation to act, while the connection withbeliefs is necessary to account for theapparent objectivity of such judgments.Arguments abound that no class of utterancescan coherently be understood as having suchconceptual connections to attitudes of bothsorts, hence that an inconsistency results. Buton Davidson's account assertions of evaluativejudgments have just such connections to boththe relevant desire and a belief concerning anevaluative matter of fact. I argue that thisaccount has the resources to respond tostandard objections, and at least meritsconsideration as one among other plausiblealternatives.     

Conclusive Reasons and Epistemic Luck

What is it to have conclusive reasons to believe a proposition P? According to a view famously defended by Dretske, a reason R is conclusive for P just in case [R would not be the case unless P were the case]. I argue that, while knowing that P is plausibly related to having conclusive reasons to believe that P, having such reasons cannot be understood in terms of the truth of this counterfactual condition. Simple examples show that it is possible to believe P on the basis of reasons that satisfy the counterfactual, and still get things right about P only as a matter of luck. Seeing where this account of conclusive reasons goes wrong points to an important distinction between having conclusive reasons and relying on reasons that are in point of fact conclusive. It also has wider consequences for whether modal principles like sensitivity and safety can rule out the pernicious kind of epistemic luck, or the kind of luck that interferes with knowledge.     

Necessity and Relative Contingency

The paper introduces a contingential language extended with a propositional constant τ axiomatized in a system named KΔτ , which receives a semantical analysis via relational models. A definition of the necessity operator in terms of Δ and τ allows proving (i) that KΔτ is equivalent to a modal system named K□τ (ii) that both KΔτ and K□τ are tableau-decidable and complete with respect to the defined relational semantics (iii) that the modal τ -free fragment of KΔτ is exactly the deontic system KD. In §4 it is proved that the modal τ -free fragment of a system KΔτw weaker than KΔτ is exactly the minimal normal system K. Presented by Daniele Mundici