共查询到19条相似文献,搜索用时 109 毫秒
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基于逻辑关系的数学模型—逻辑模型的理论与分析 总被引:1,自引:1,他引:0
孟波 《数学的实践与认识》2009,39(24)
用数学模型研究实际问题是现代科学研究的常用方法.通常采用的数学模型是各种方程.但是使用方程作为研究手段也存在着许多问题,例如无法应用于不可计算的或者不具有数量概念的实际情况中,这样许多问题无法加以讨论.以命题为基础,通过数理逻辑的概念和方法,建立了具有实际意义的逻辑模型的一般理论,分析了逻辑模型的一些基本性质.逻辑模型可以看成传统模型的一种推广. 相似文献
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简易逻辑是新教材中新增加的内容,这部分内容主要涉及逻辑学中最基本、最简单的知识,目的是让学生能使用逻辑规划来弄清楚命题之间的逻辑关系.其中逻辑联结词“或”、“且”、“非”及简单命题、复合命题等概念的理解,命题的真假判断与应用,四种命题及其关系,充要条件的概念及两命题间充要关系的判断与证明,不仅是每年高考关注的热点,也是同学们在学习时容易产生误解的地方.[第一段] 相似文献
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简易逻辑知识解读点滴 总被引:2,自引:0,他引:2
数学是一门逻辑性很强的学科 .学习数学时 ,处处涉及命题之间的逻辑关系和推理论证 .高中数学新教材“简易逻辑”结合中学数学内容 ,介绍一些简单而又实用的逻辑知识 ,使学生进一步弄清命题与命题之间的逻辑关系 ,增强判断是非的能力和推理能力 ,避免一些易犯的逻辑错误 ,从而有助于学生学好数学 .但作为我们中学数学一线教师 ,往往都没有系统地学习过逻辑学 ,对逻辑知识存在一定的认知缺陷 .本文结合自身的教学实践 ,谈点肤浅的认识 ,敬请同仁斧正 .1 命题与判断初高中共有两次命题的定义 ,初中数学为了便于学生接受 ,给命题下的定义是 :… 相似文献
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在简易逻辑的教学中 ,常因为对逻辑联结词的使用不当而导致一些错解 .本文将就一些常见的错解进行分析 ,供读者参考 .例 1 p :9的平方根是 3.写出非 p并判断真假 .错解 有人认为非 p是“9的平方根不是 3” .并认为“9的平方根不是 3”是一个假命题 ,从而出现p与非 p均是假命题 .上述解法中存在两个问题 .①非 p的写法不正确 .一个命题的否定并非是在命题的结论前添加否定词就能完成的 .正如文 [1]所指出的那样 ,当命题中含有全称量词或存在量词时 ,命题的否定应对量词作适当的调整 .事实上 ,例 1中的命题 p隐含着全称量词 ,p等价… 相似文献
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逻辑证明在高等数学及其教学中占有重要地位,本着重从间接证明尤其是反证法的逻辑结构入手,剖析了高等数学中的范例,反证法离不开充分条件假言推理的否定后件式,其中的后件“q”可以是直言命题或关系命题,也可以是联言命题,选言命题,假言命题和负命题。 相似文献
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对逻辑联结词再理解 总被引:3,自引:0,他引:3
高中数学新教材“简易逻辑”中规定 :“或”、“且”、“非”这些词叫做逻辑联结词 .不含逻辑联结词的命题是简单命题 .由简单命题与逻辑联结词构成的命题是复合命题 .根据以上定义 ,如何解释“方程 (x - 1 )(x - 2 ) =0的根是x =1或x =2”是简单命题还是复合命题呢 ?如果是简单命题 ,那么又怎样对语句中的“或”作解释呢 ?如果是复合命题 ,那么由“方程 (x - 1 )(x - 2 ) =0的根是x =1”是假命题 ,“方程(x - 1 ) (x - 2 ) =0的根是x =2”也是假命题得 :复合命题“方程 (x - 1 ) (x - 2 ) =0的根是x =1或x =2”也是假命题 .… 相似文献
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A. D. Yashin 《Algebra and Logic》2003,42(3):207-216
We give an exhaustive classification of Novikov complete extensions of the intuitionistic propositional logic in a language with extra logical constants. 相似文献
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In this paper, credibilistic logic is introduced as a new branch of uncertain logic system by explaining the truth value of
fuzzy formula as credibility value. First, credibilistic truth value is introduced on the basis of fuzzy proposition and fuzzy
formula, and the consistency between credibilistic logic and classical logic is proved on the basis of some important properties
about truth values. Furthermore, a credibilistic modus ponens and a credibilistic modus tollens are presented. Finally, a
comparison between credibilistic logic and possibilistic logic is given. 相似文献
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We propose a first approximation to the modeling of cognitive decisions based on the theory of associative memories. The basic structure are the matrix memories of Anderson-Kohonen adapted to include the modulation of associations via tensorial preprocessing of inputs. This view admits an easy implementation of logical operations as matrix operators. From this “vectorial logic” springs a variety of models for fuzzy decision processes. Degrees of fuzziness are introduced at two different levels: (a) by the operators of modal logic, and (b) by using logical variables as vectors with projections inside the interval [0, 1]. The outcomes of this vectorial logic can be projected onto unit vectors yielding scalar difference equations. As examples we study the dynamics of contradictory self-referential systems and processes leading to competition between options. These models exhibit a variety of dynamical patterns that include stable steady states, oscillations, and deterministic chaos. © 1997 John Wiley & Sons, Inc. 相似文献
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Eduardo Mizraji 《Mathematical Logic Quarterly》1996,42(1):27-40
Vector logic is a mathematical model of the propositional calculus in which the logical variables are represented by vectors and the logical operations by matrices. In this framework, many tautologies of classical logic are intrinsic identities between operators and, consequently, they are valid beyond the bivalued domain. The operators can be expressed as Kronecker polynomials. These polynomials allow us to show that many important tautologies of classical logic are generated from basic operators via the operations called Type I and Type II products. Finally, it is described a matrix version of the Fredkin gate that extends its properties to the many-valued domain, and it is proved that the filtered Fredkin operators are second degree Kronecker polynomials that cannot be generated by Type I or Type II products. Mathematics Subject Classification: 03B05, 03B50. 相似文献
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Aimable-André Dufatanye 《Logica Universalis》2012,6(1-2):45-67
The square of opposition and many other geometrical logical figures have increasingly proven to be applicable to different fields of knowledge. This paper seeks to show how Blanché generalizes the classical theory of oppositions of propositions and extends it to the structure of opposition of concepts. Furthermore, it considers how Blanché restructures the Apuleian square by transforming it into a hexagon. After presenting G. Kalinowski??s formalization of Blanché??s hexagonal theory, an illustration of its applicability to mathematics, to modal logic, and to the logic of norms is depicted. The paper concludes by criticizing Blanché??s claim according to which, his logical hexagon can be considered as the objective basis of the structure of the organisation of concepts, and as the formal structure of thought in general. It is maintained that within the frame of diagrammatic reasoning Blanché??s hexagon keeps its privileged place as a ??nice?? and useful tool, but not necessarily as a norm of thought. 相似文献
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Logic is a popular word in the social sciences, but it is rarely used as a formal tool. In the past, the logical formalisms were cumbersome and difficult to apply to domains of purposeful action. Recent years, however, have seen the advance of new logics specially designed for representing actions. We present such a logic and apply it to a classical organization theory, J.D. Thompson's Organizations in Action. The working hypothesis is that formal logic draws attention to some finer points in the logical structure of a theory, points that are easily neglected in the discursive reasoning typical for the social sciences. Examining Organizations in Action we find various problems in its logical structure that should, and, as we argue, could be addressed. 相似文献
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“Setting” n-Opposition 总被引:1,自引:1,他引:0
Régis Pellissier 《Logica Universalis》2008,2(2):235-263
Our aim is to show that translating the modal graphs of Moretti’s “n-opposition theory” (2004) into set theory by a suited device, through identifying logical modal formulas with appropriate
subsets of a characteristic set, one can, in a constructive and exhaustive way, by means of a simple recurring combinatory,
exhibit all so-called “logical bi-simplexes of dimension n” (or n-oppositional figures, that is the logical squares, logical hexagons, logical cubes, etc.) contained in the logic produced
by any given modal graph (an exhaustiveness which was not possible before). In this paper we shall handle explicitly the classical
case of the so-called 3(3)-modal graph (which is, among others, the one of S5), getting to a very elegant tetraicosahedronal
geometrisation of this logic.
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