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基于泛逻辑学的柔性命题逻辑研究 总被引:6,自引:0,他引:6
现有的数理逻辑是刚性逻辑,不能满足研究不确定性问题的需要.概率测度是研究不确定性问题的重要数学工具.但作为概率推理理论基础的概率逻辑发展不够成熟,影响了它在不确定性推理中的广泛应用.本文第二作者在探索包含确定性和各种不确定性的现实世界逻辑规律的基础上.建立一个包容刚性逻辑和柔性逻辑的命题泛逻辑学体系.本文利用这一研究成果,对命题概率逻辑进行了探讨. 相似文献
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当前,世界各主要大国都把人工智能作为它们的国家战略。人工智能的发展正在快速改变着人类的生活方式和思想观念。在中国,有一小批研究者20多年来一直在基于辩证唯物主义潜心研究具有普适性的人工智能基础理论,包括智能的形成机制、逻辑基础、数学基础、协调机理、矛盾转化等。终于,他们各自建立了机制主义人工智能理论、泛逻辑学理论、因素空间理论、协调学、可拓学、集对分析等。其中,机制主义人工智能理论是基于智能形成机制的通用理论,它能把现有的结构主义、功能主义和行为主义三大流派有机地统一起来,使意识、情感、理智成为三位一体的关系;因素空间理论是机制主义人工智能理论的数学基础;泛逻辑学理论是机制主义人工智能理论的逻辑基础。本文介绍了泛逻辑学理论的基本思想、理论基础和应用方法,阐明它的理论意义和应用价值。特别需要指出的是,在广义概率论基础上建立的命题泛逻辑(包括刚性逻辑和柔性逻辑),可看成一个完整的命题级智能信息处理算子库,库中完整地包含了全部18种柔性信息处理模式(包括16种布尔信息处理模式),可用类型编码<a,b,e>来严格区分,用它可寻找到适合自己的信息处理算子完整簇来使用。在每一个信息处理模式中,各种不确定性的组合状态由不确定性程度属性编码<k,h,β,e>来严格区分,用它可在本信息处理模式的算子完整簇中精确选择具体的算子来使用。这表明柔性信息处理本质上是一把密码锁,它需要专门的密码<a,b,e>+<k,h,β,e>才能正常打开,不能乱点鸳鸯谱。通过只有18种模式,每种模式可以从最大算子连续变化到最小算子,已经证明了没有一个命题算子被遗漏。 相似文献
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人工智能中泛逻辑学的研究* 总被引:2,自引:0,他引:2
逻辑学的理论为人工智能的发展提供了有力的工具。标准逻辑促进了人工智能早期的发展,随着处理知识的随机性、模糊性和未知性等特点的出现,模糊逻辑等在人工智能中得到发展;各种形式的非标准逻辑的出现,促使建立尽可能包容一切逻辑形态和推理模式的泛逻辑学。在分析模糊逻辑规律的基础上,把三角范数理论和逻辑学紧密结合起来,利用三角范数理论提出命题泛逻辑学。目前,泛逻辑学在人工智能中已经取得了一定的研究成果。 相似文献
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模糊逻辑是许多实际应用的逻辑基础,但是其理论基础还不太成熟,不能够实现真正的柔性,这也就影响了它的应用范围.逻辑学正处于第二次革命中,也就是由刚性逻辑到柔性逻辑的转变,泛逻辑学正是由何华灿教授建立的一种新的柔性逻辑体系.只有在泛逻辑学的框架内才能真正实现模糊逻辑关系的柔性化. 相似文献
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基于泛逻辑学的概率命题逻辑的研究与分析 总被引:3,自引:0,他引:3
概率逻辑是不确定推理的一个重要逻辑基础,但其目前还不太完善.泛逻辑学是何华灿教授在探索各种不确定性问题求解中建立起来的一种新的柔性逻辑体系.理论上,概率逻辑仅是泛逻辑学的一个特例.在对目前比较典型的几种概率逻辑模型进行分析的基础上,基于命题泛逻辑学的思想和方法,指出了概率命题逻辑中存在的一些主要问题,探讨了解决这些问题的思路与方法。 相似文献
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人工智能科学中的概率逻辑 总被引:1,自引:0,他引:1
人工智能科学,从其诞生之日起便与逻辑学密不可分。本文首先对逻辑学的分类、相互关系以及泛逻辑的概念等进行了讨论,并对人工智能中逻辑学的应用及发展进行了必要的分析。然后讲述了逻辑学与概率论两大理论基础之上的不确定性推理方法——概率逻辑,重点研究了二值概率逻辑与三值概率逻辑。最后阐述了概率逻辑在人工智能科学中的应用以及对它的思考。 相似文献
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柔性逻辑学的研究目标是探索逻辑的一般规律,它指出命题真值误差用连续变化的广义自相关系数k∈[0,1]来刻画。在柔性逻辑的不确定推理中,N范数是一级运算的数理模型。由于在现实生活中,很多逻辑推理控制必须在其自身的定义域内完成,因此以三角范数作为柔性逻辑学研究的数学工具,定义了[0,∞]区间上的N范数和N性生成元,并研究了相关主要性质;证明了N范数生成定理;给出了广义自相关系数的计算方法;证明了[0,∞]区间上指数(幂)型N性生成元为N性生成元完整簇;从而为柔性逻辑中[0,∞]区间的一级运算模型提供了重要的理论基础。 相似文献
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The epistemic notions of knowledge and belief have most commonly been modeled by means of possible worlds semantics. In such approaches an agent knows (or believes) all logical consequences of its beliefs. Consequently, several approaches have been proposed to model systems of explicit belief, more suited to modeling finite agents or computers. In this paper a general framework is developed for the specification of logics of explicit belief. A generalization of possible worlds, called situations, is adopted. However the notion of an accessibility relation is not employed; instead a sentence is believed if the explicit proposition expressed by the sentence appears among a set of propositions associated with an agent at a situation. Since explicit propositions may be taken as corresponding to "belief contexts" or "frames of mind," the framework also provides a setting for investigating such approaches to belief. The approach provides a uniform and flexible basis from which various issues of explicit belief may be addressed and from which systems may be contrasted and compared. A family of logics is developed using this framework, which extends previous approaches and addresses issues raised by these earlier approaches. The more interesting of these logics are tractable, in that determining if a belief follows from a set of beliefs, given certain assumptions, can be accomplished in polynomial time. 相似文献
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The language of signed formulas offers a first-order classical logic framework for automated reasoning in multiple-valued logics. It is sufficiently general to include both annotated logics and fuzzy operator logics. Signed resolution unifies the two inference rules of annotated logics, thus enabling the development of an SLD-style proof procedure for annotated logic programs. Signed resolution also captures fuzzy resolution. The logic of signed formulas offers a means of adapting most classical inference techniques to multiple-valued logics. 相似文献
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Logical connectives familiar from the study of hybrid logic can be added to the logical framework LF, a constructive type theory of dependent functions. This extension turns out to be an attractively simple one, and maintains all the usual theoretical and algorithmic properties, for example decidability of type-checking. Moreover it results in a rich metalanguage for encoding and reasoning about a range of resource-sensitive substructural logics, analagous to the use of LF as a metalanguage for more ordinary logics.This family of applications of the language, contrary perhaps to expectations of how hybridized systems are typically used, does not require the usual modal connectives box and diamond, nor any internalization of a Kripke accessibility relation. It does, however, make essential use of distinctively hybrid connectives: universal quantifiation over worlds, truth of a proposition at a named world, and local binding of the current world. This supports the claim that the innovations of hybrid logic have independent value even apart from their traditional relationship to temporal and alethic modal logics. 相似文献
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We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. 相似文献