On Reduction Rules,Meaning-as-use,and Proof-theoretic Semantics

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. Presented by Heinrich Wansing     

邵康节的易学思想

本文以现代日本学者的眼光对邵雍的易学思想作了较为系统的论述。认为邵雍从宇宙观和世界观的理论基础上推演出他的历史观来 ,企图把宇宙世界的生成、万物的存在以及历史的变迁都还原为抽象的数 ,因而一方面难免陷入脱离事实、空洞推演的弊端 ,而在另方面又增加了重视义理以指导人事的内容。所以他的易学思想在古代术数与宋明理学之间 ,起了继往开来的重大作用     

条件推理中的命题语义加工

本研究运用五种不同情境内容的大前提和四种不同逻辑形式的小前提,组成２０种条件推理题,对１２７名大学生进行了测试,力图研究不同命题内容对不同形式的逻辑推理的影响,并进而探讨人们在条件推理中对前提进行语义加工的机制．本文提出了前提语义加工的“问题空间“的解释．     

Marginalia on Sequent Calculi

The paper discusses the relationship between normal natural deductions and cutfree proofs in Gentzen (sequent) calculi in the absence of term labeling. For Gentzen calculi this is the usual version; for natural deduction this is the version under the complete discharge convention, where open assumptions are always discharged as soon as possible. The paper supplements work by Mints, Pinto, Dyckhoff, and Schwichtenberg on the labeled calculi.     

Causality assessment in epidemiology

Epidemiology relies upon a broad interpretation of determinism. This paper discusses analogies with the evolution of the concept of cause in physics, and analyzes the classical nine criteria proposed by Sir Austin Bradford Hill for causal assessment. Such criteria fall into the categories of enumerative induction, eliminative induction, deduction and analogy. All of these four categories are necessary for causal assessment and there is no natural hierarchy among them, although a deductive analysis of the study design is preliminary to any assessment.     

Frege's Content-Principle and Relevant Deducibility

Given the harmony principle for logical operators, compositionality ought to ensure that harmony should obtain at the level of whole contents. That is, the role of a content qua premise ought to be balanced exactly by its role as a conclusion. Frege's contextual definition of propositional content happens to exploit this balance, and one appeals to the Cut rule to show that the definition is adequate.We show here that Frege's definition remains adequate even when one relevantizes logic by abandoning an unrestricted Cut rule. The proof exploits the fact that in the relevantized logic, which abandons the unrestricted rule of Cut, any failure of the transitivity of deduction is offset by the epistemic gain involved in learning that a stronger-than-expected result holds.     

Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices. Dedicated to the memory of Willem Johannes Blok     

Generalized Logical Consequence: Making Room for Induction in the Logic of Science

We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logical consequence are also presented.