共查询到19条相似文献,搜索用时 78 毫秒
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在语言真值格值一阶逻辑系统的框架下,讨论了两种推理模型中的不确定性推理理论与方法,并针对不同的推理规则得到了推理算法,其推理算法既有合理的语义解释又有严密的语法论证. 相似文献
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积逻辑系统中的广义重言式 总被引:15,自引:2,他引:13
讨论积逻辑系统中的广义重言式理论 ,给出积逻辑系统中子代数和广义重言式的一系列性质。本文的主要结果表明 ,在几个重要的逻辑系统中 ,标准积逻辑系统具有最简单的广义重言式结构 ,而在推理过程中 ,它具有较差的真值传递性。 相似文献
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在模糊逻辑系统中提出了广义有效推理;根据积分真度的性质,证明了广义有效推理的积分真度递减定理,从而在模糊逻辑系统中实现了根据推理前提的真度计算推理结论的真度;最后,把真度递减定理与利用斐波那契数列对推理结论真度的推算结果进行了对比,说明了真度递减定理的优越性. 相似文献
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根据信息理论的一些基本观点首次定义了决策逻辑系统中公式的信息熵,由此给出了知识系统中推理规则信息熵的定义。然后讨论了推理规则信息熵的某些性质。随后又建立了一些推理规则信息熵有关的若干重要概念,从而揭示了信息论与知识表达系统之间的某些联系,为信息理论应用于人工智能及数据挖掘提供了一定的理论或技术性工具。 相似文献
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讨论基于语言真值格值一阶逻辑的不确定性推理的语法内容,并研究了推理规则的用性和可靠性,证明了推理规则在a≤∧θ∈Lx×L2(θ→θ')(θ≠(ax,b2))水平下的闭性,得到了推理规则在此水平下可靠性的充分必要务件. 相似文献
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《Fuzzy Sets and Systems》2004,145(2):213-228
In this paper, a rather expressive fuzzy temporal logic for linear time is introduced. First, this logic is a multivalued generalization (Lukasiewicz style) of a two-valued linear-time temporal logic based on, e.g., the “until” operator. Second, it is obtained by introducing a generalized time quantifier (a generalization of the partition operator investigated by Shen) applied to fuzzy time sets.In this fuzzy temporal logic, generalized compositional rules of inference, suitable for approximate reasoning in a temporal setting, are presented as valid formulas.Some medical examples illustrate our approach. 相似文献
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João Rasga Wafik Boulos Lotfallah Cristina Sernadas 《Mathematical Logic Quarterly》2013,59(4-5):286-302
We give an axiomatization of first‐order logic enriched with the almost‐everywhere quantifier over finitely additive measures. Using an adapted version of the consistency property adequate for dealing with this generalized quantifier, we show that such a logic is both strongly complete and enjoys Craig interpolation, relying on a (countable) model existence theorem. We also discuss possible extensions of these results to the almost‐everywhere quantifier over countably additive measures. 相似文献
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Radosav Djordjevic Nebojša Ikodinović Žarko Mijajlović 《Archive for Mathematical Logic》2007,46(1):1-8
A topological class logic is an infinitary logic formed by combining a first-order logic with the quantifier symbols O and
C. The meaning of a formula closed by quantifier O is that the set defined by the formula is open. Similarly, a formula closed
by quantifier C means that the set is closed. The corresponding models are a topological class spaces introduced by Ćirić
and Mijajlović (Math Bakanica 1990). The completeness theorem is proved.
This research was supported by the Ministry of Science, Technology and Development, Republic of Serbia, through Mathematical
Institute, under grant 144013. 相似文献
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We give a sufficient condition for the inexpressibility of the k-th extended vectorization of a generalized quantifier in , the extension of first-order logic by all k-ary quantifiers. The condition is based on a model construction which, given two -equivalent models with certain additional structure, yields a pair of -equivalent models. We also consider some applications of this condition to quantifiers that correspond to graph properties,
such as connectivity and planarity.
Received: 15 October 1996 相似文献
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进一步研究模糊推理的非模糊形式,在几个重要的逻辑系统中形式地讨论GMP(广义取式)和GMT(广义拒取式)问题的最优解。结果表明,GMP和GMT问题的三I解和一种新的三I解都是某种意义下的最优解。还讨论所给算法的还原性问题。 相似文献
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Mingsheng Ying 《Mathematical Logic Quarterly》1992,38(1):197-201
In [This Zeitschrift 25 (1979), 45-52, 119-134, 447-464], Pavelka systematically discussed propositional calculi with values in enriched residuated lattices and developed a general framework for approximate reasoning. In the first part of this paper we introduce the concept of generalized quantifiers into Pavelka's logic and establish the fundamental theorem of ultraproduct in first order Pavelka's logic with generalized quantifiers. In the second part of this paper we show that the fundamental theorem of ultraproduct in first order Pavelka's logic is preserved under some direct product of lattices of truth values. 相似文献
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Kerkko Luosto 《Archive for Mathematical Logic》2012,51(3-4):241-255
Vectorization of a class of structures is a natural notion in finite model theory. Roughly speaking, vectorizations allow tuples to be treated similarly to elements of structures. The importance of vectorizations is highlighted by the fact that if the complexity class PTIME corresponds to a logic with reasonable syntax, then it corresponds to a logic generated via vectorizations by a single generalized quantifier (Dawar in J Log Comput 5(2):213–226, 1995). It is somewhat surprising, then, that there have been few systematic studies of the expressive power of vectorizations of various quantifiers. In the present paper, we consider the simplest case: the cardinality quantifiers C S . We show that, in general, the expressive power of the vectorized quantifier logic ${{\rm FO}(\{{\mathsf C}_S^{(n)}\, | \, n \in \mathbb{Z}_+\})}$ is much greater than the expressive power of the non-vectorized logic FO(C S ). 相似文献
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Mikhail Sheremet 《Annals of Pure and Applied Logic》2010,161(4):534-559
We propose and investigate a uniform modal logic framework for reasoning about topology and relative distance in metric and more general distance spaces, thus enabling the comparison and combination of logics from distinct research traditions such as Tarski’s S4 for topological closure and interior, conditional logics, and logics of comparative similarity. This framework is obtained by decomposing the underlying modal-like operators into first-order quantifier patterns. We then show that quite a powerful and natural fragment of the resulting first-order logic can be captured by one binary operator comparing distances between sets and one unary operator distinguishing between realised and limit distances (i.e., between minimum and infimum). Due to its greater expressive power, this logic turns out to behave quite differently from both S4 and conditional logics. We provide finite (Hilbert-style) axiomatisations and ExpTime-completeness proofs for the logics of various classes of distance spaces, in particular metric spaces. But we also show that the logic of the real line (and various other important metric spaces) is not recursively enumerable. This result is proved by an encoding of Diophantine equations. 相似文献