Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation

Constructive logic with Nelson negation is an extension of the intuitionistic logic with a special type of negation expressing some features of constructive falsity and refutation by counterexample. In this paper we generalize this logic weakening maximally the underlying intuitionistic negation. The resulting system, called subminimal logic with Nelson negation, is studied by means of a kind of algebras called generalized N-lattices. We show that generalized N-lattices admit representation formalizing the intuitive idea of refutation by means of counterexamples giving in this way a counterexample semantics of the logic in question and some of its natural extensions. Among the extensions which are near to the intuitionistic logic are the minimal logic with Nelson negation which is an extension of the Johansson's minimal logic with Nelson negation and its in a sense dual version — the co-minimal logic with Nelson negation. Among the extensions near to the classical logic are the well known 3-valued logic of Lukasiewicz, two 12-valued logics and one 48-valued logic. Standard questions for all these logics — decidability, Kripke-style semantics, complete axiomatizability, conservativeness are studied. At the end of the paper extensions based on a new connective of self-dual conjunction and an analog of the Lukasiewicz middle value ½ have also been considered.     

Gentzen-Type Methods for Bilattice Negation

A general Gentzen-style framework for handling both bilattice (or strong) negation and usual negation is introduced based on the characterization of negation by a modal-like operator. This framework is regarded as an extension, generalization or re- finement of not only bilattice logics and logics with strong negation, but also traditional logics including classical logic LK, classical modal logic S4 and classical linear logic CL. Cut-elimination theorems are proved for a variety of proposed sequent calculi including CLS (a conservative extension of CL) and CLS_cw (a conservative extension of some bilattice logics, LK and S4). Completeness theorems are given for these calculi with respect to phase semantics, for SLK (a conservative extension and fragment of LK and CLS_cw, respectively) with respect to a classical-like semantics, and for SS4 (a conservative extension and fragment of S4 and CLScw, respectively) with respect to a Kripke-type semantics. The proposed framework allows for an embedding of the proposed calculi into LK, S4 and CL.     

The Class of Extensions of Nelson's Paraconsistent Logic

The article is devoted to the systematic study of the lattice εN4_⊥ consisting of logics extending N4_⊥. The logic N4_⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4_⊥ and the lattice of superintuitionistic logics. Distinguish in εN4_⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate. The author acknowledges support by the Alexander von Humboldt-Stiftung and by Counsil for Grants under RF President, project NSh - 2112.2003.1.     

高血压病用药模式的更迭与发展

从辩证的否定观角度分析了高血压病用药模式的更迭与发展,倡导“循证医学指导-基因导向型”的新型用药模式,以寻求解决目前高血压病临床用药实际工作中遇到的困难和问题。     

Harmony and Autonomy in Classical Logic

Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use.I argue that Dummett gives a mistaken elaboration of the notion of harmony, an idea stemming from a remark of Gerhard Gentzen"s. The introduction-rules are autonomous if they are taken fully to specify the meaning of the logical constants, and the rules are harmonious if the elimination-rule draws its conclusion from just the grounds stated in the introduction-rule. The key to harmony in classical logic then lies in strengthening the theory of the conditional so that the positive logic contains the full classical theory of the conditional. This is achieved by allowing parametric formulae in the natural deduction proofs, a form of multiple-conclusion logic.     

The Pleasures of Anticipation: Enriching Intuitionistic Logic

We explore a relation we call anticipation between formulas, where A anticipates B (according to some logic) just in case B is a consequence (according to that logic, presumed to support some distinguished implicational connective ) of the formula AB. We are especially interested in the case in which the logic is intuitionistic (propositional) logic and are much concerned with an extension of that logic with a new connective, written as a, governed by rules which guarantee that for any formula B, aB is the (logically) strongest formula anticipating B. The investigation of this new logic, which we call ILa, will confront us on several occasions with some of the finer points in the theory of rules and with issues in the philosophy of logic arising from the proposed explication of the existence of a connective (with prescribed logical behaviour) in terms of the conservative extension of a favoured logic by the addition of such a connective. Other points of interest include the provision of a Kripke semantics with respect to which ILa is demonstrably sound, deployed to establish certain unprovability results as well as to forge connections with C. Rauszer's logic of dual intuitionistic negation and dual intuitionistic implication, and the isolation of two relations (between formulas), head-implication and head-linkage, which, though trivial in the setting of classical logic, are of considerable significance in the intuitionistic context.     

A Pragmatic Case against Pragmatic Scientific Realism

Pragmatic Scientific Realism (PSR) urges us to take up the realist aim or the goal of truth although we have good reason to think that the goal can neither be attained nor approximated. While Newton-Smith thinks that pursuing what we know we cannot achieve is clearly irrational, Rescher disagrees and contends that pursuing an unreachable goal can be rational on pragmatic grounds—if in pursuing the unreachable goal one can get indirect benefits. I have blocked this attempt at providing a pragmatic justification for the realist aim of PSR on precisely the same pragmatic grounds—since there is a competing alternative to PSR, and the alternative can provide whatever indirect benefits PSR can offer while being less risky than it is, prudential reasoning favours the alternative to PSR. This undermines the pragmatic case for the realist aim of science since the instrumentalist alternative does not aim at the truth.     

A Note on Negation in Categorial Grammar

A version of strong negation is introduced into Categorial Grammar.The resulting syntactic calculi turn out to be systems of connexivelogic.     

认知越灵活，句子理解越快?

采用威斯康星卡片分类测验、语法–语义灵活性任务和语义肯定性任务,以47名大学生为研究对象,考察一般认知灵活性、语法–语义灵活性与句子理解的关系。控制性别作用后,回归分析结果显示：（1）一般认知灵活性只显著预测一般肯定句理解速度,语法–语义灵活性显著预测一般肯定、一般否定、肯定反问、否定反问、双重否定和三重否定句理解速度;（2）语法–语义灵活性比一般认知灵活性对一般肯定句理解速度的预测作用更大;（3）语法–语义灵活性对肯定反问句比对否定反问句理解速度的预测作用更大。这表明语法–语义灵活性比一般认知灵活性对句子理解速度的贡献更大,且认知灵活性对不同句式句子理解速度的影响不同。