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1.
In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in the k-degree symmetric group Sk, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p-valued logic functions are determined, where p is a prime. Mathematics Subject Classification: 03B50, 20B35. 相似文献
2.
Ming Sheng Ying 《数学学报(英文版)》2001,17(1):89-102
We use a semantical method of complete residuated lattice-valued logic to give a generalization of fuzzy topology as a partial
answer to a problem by Roser and Turquette.
This work is supported by the National Foundation for Distinguished Young Scholars (Grant No: 69725004),
Research and Development Project of High-Technology (Grant No: 863-306-ZT06-04-3) and Foundation of
Natural Sciences (Grant No: 69823001) of China and Fok Ying-Tung Education Foundation 相似文献
3.
Frank Wolter 《Mathematical Logic Quarterly》1996,42(1):145-171
4.
Esko Turunen 《Mathematical Logic Quarterly》1995,41(2):236-248
A many-valued sentential logic with truth values in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper develops some ideas of Goguen and generalizes the results of Pavelka on the unit interval. The proof for completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if and only if the algebra of the truth values is a complete MV-algebra. In the well-defined fuzzy sentential logic holds the Compactness Theorem, while the Deduction Theorem and the Finiteness Theorem in general do not hold. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. 相似文献
5.
Disturbing Fuzzy Propositional Logic and its Operators 总被引:1,自引:0,他引:1
Xin Liu 《Fuzzy Optimization and Decision Making》2006,5(2):163-175
In this paper, the concept of disturbing fuzzy propositional logic is introduced, and the operators of disturbing fuzzy propositions
is defined. Then the 1-dimensional truth value of fuzzy logic operators is extended to be two-dimensional operators, which
include disturbing fuzzy negation operators, implication operators, “and” and “or” operators and continuous operators. The
properties of these logic operators are studied. 相似文献
6.
Alexej P. Pynko 《Mathematical Logic Quarterly》1995,41(4):442-454
The aim of this paper is technically to study Belnap's four-valued sentential logic (see [2]). First, we obtain a Gentzen-style axiomatization of this logic that contains no structural rules while all they are still admissible in the Gentzen system what is proved with using some algebraic tools. Further, the mentioned logic is proved to be the least closure operator on the set of {Λ, V, ?}-formulas satisfying Tarski's conditions for classical conjunction and disjunction together with De Morgan's laws for negation. It is also proved that Belnap's logic is the only sentential logic satisfying the above-mentioned conditions together with Anderson-Belnap's Variable-Sharing Property. Finally, we obtain a finite Hilbert-style axiomatization of this logic. As a consequence, we obtain a finite Hilbert-style axiomatization of Priest's logic of paradox (see [12]). 相似文献
7.
In this paper, closure operators of lattice-valued propositional logic LP(X) are studied. A family of classical closure operators are defined and the relation between them and closure operators of LP(X) is investigated. At the same time, a tool for checking compactness of LP(X) is given. 相似文献
8.
A logical and algebraic treatment of conditional probability 总被引:1,自引:0,他引:1
This paper is devoted to a logical and algebraic treatment of conditional probability. The main ideas are the use of non-standard probabilities and of some kind of standard part function in order to deal with the case where the conditioning event has probability zero, and the use of a many-valued modal logic in order to deal probability of an event as the truth value of the sentence is probable, along the lines of Hájeks book [H98] and of [EGH96]. To this purpose, we introduce a probabilistic many-valued logic, called FP(S), which is sound and complete with respect a class of structures having a non-standard extension [0,1] of [0,1] as set of truth values. We also prove that the coherence of an assessment of conditional probabilities is equivalent to the coherence of a suitably defined theory over FP(S) whose proper axioms reflect the assessment itself.Mathematics Subject Classification (2000): 03B50, 06D35 相似文献
9.
Josep Maria Font Àngel J. Gil Antoni Torrens Ventura Verdú 《Archive for Mathematical Logic》2006,45(7):839-868
Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen calculus. In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of “preservation of degrees of truth”. We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a structural Gentzen calculus, which is shown to be fully adequate for it. This logic is an interesting example for the general theory: it is selfextensional, non-protoalgebraic, and satisfies a “graded” deduction theorem. Moreover, the Gentzen system is algebraizable. The first deductive system mentioned turns out to be the extension of the second by the rule of Modus Ponens.While writing this paper, the authors were partially supported by grants MTM2004-03101 and TIN2004-07933-C03-02 of the Spanish Ministry of Education and Science, including FEDER funds of the European Union. 相似文献
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13.
Tommaso Flaminio 《Archive for Mathematical Logic》2007,46(3-4):301-319
In this paper we investigate the problem of testing the coherence of an assessment of conditional probability following a
purely logical setting. In particular we will prove that the coherence of an assessment of conditional probability χ can be
characterized by means of the logical consistency of a suitable theory T
χ defined on the modal-fuzzy logic FP
k
(RŁΔ) built up over the many-valued logic RŁΔ. Such modal-fuzzy logic was previously introduced in Flaminio (Lecture Notes in Computer Science, vol. 3571, 2005) in order
to treat conditional probability by means of a list of simple probabilities following the well known (smart) ideas exposed
by Halpern (Proceedings of the eighth conference on theoretical aspects of rationality and knowledge, pp 17–30, 2001) and
by Coletti and Scozzafava (Trends Logic 15, 2002). Roughly speaking, such logic is obtained by adding to the language of RŁΔ a list of k modalities for “probably” and axioms reflecting the properties of simple probability measures. Moreover we prove that the satisfiability problem for
modal formulas of FP
k
(RŁΔ) is NP-complete. Finally, as main result of this paper, we prove FP
k
(RŁΔ) in order to prove that the problem of establishing the coherence of rational assessments of conditional probability is NP-complete.
相似文献
14.
Hiroshi Aoyama 《Mathematical Logic Quarterly》1998,44(2):167-175
In this paper we will study a formal system of intuitionistic modal predicate logic. The main result is its semantic completeness theorem with respect to algebraic structures. At the end of the paper we will also present a brief consideration of its syntactic relationships with some similar systems. 相似文献
15.
Ramón Béjar 《Discrete Applied Mathematics》2007,155(12):1613-1626
Regular-SAT is a constraint programming language between CSP and SAT that—by combining many of the good properties of each paradigm—offers a good compromise between performance and expressive power. Its similarity to SAT allows us to define a uniform encoding formalism, to extend existing SAT algorithms to Regular-SAT without incurring excessive overhead in terms of computational cost, and to identify phase transition phenomena in randomly generated instances. On the other hand, Regular-SAT inherits from CSP more compact and natural encodings that maintain more the structure of the original problem. Our experimental results—using a range of benchmark problems—provide evidence that Regular-SAT offers practical computational advantages for solving combinatorial problems. 相似文献
16.
Rostislav Horĉík 《Archive for Mathematical Logic》2005,44(4):413-424
MTL is a schematic extension of the monoidal t-norm based logic (MTL) by the characteristic axioms of product logic. In this paper we prove that MTL satisfies the standard completeness theorem. From the algebraic point of view, we show that the class of MTL-algebras (bounded commutative cancellative residuated l-monoids) in the real unit interval [0,1] generates the variety of all MTL-algebras.The work was supported by the Grant Agency of the Czech Republic under projects GACR 201/02/1540, 401/03/H047, and by Net CEEPUS SK-042.Set offprint requests to: Rostislav Horík 相似文献
17.
In this paper we prove a bounded translation of intuitionistic propositional logic into basic propositional logic. Our new theorem, compared with the translation theorem in [1], has the advantage that it gives an effective bound on the translation, depending on the complexity of formulas. 相似文献
18.
Martina Fedel Hykel Hosni Franco Montagna 《International Journal of Approximate Reasoning》2011,52(8):1147-1170
Whilst supported by compelling arguments, the representation of uncertainty by means of (subjective) probability does not enjoy a unanimous consensus. A substantial part of the relevant criticisms point to its alleged inadequacy for representing ignorance as opposed to uncertainty. The purpose of this paper is to show how a strong justification for taking belief as probability, namely the Dutch Book argument, can be extended naturally so as to provide a logical characterization of coherence for imprecise probability, a framework which is widely believed to accommodate some fundamental features of reasoning under ignorance. The appropriate logic for our purposes is an algebraizable logic whose equivalent algebraic semantics is a variety of MV-algebras with an additional internal unary operation representing upper probability (these algebras will be called UMV-algebras). 相似文献
19.
因为"取大取小"不是数学计算,所以基于"取大取小"的模糊逻辑不能为数值转换提供算法支撑,使得模糊理论面临无合适模型可用的被动境地.指出,模糊逻辑是逻辑的一个新的近似推理研究方向,它的量化方法是数值计算;目的是支撑隶属度转换,使得由指标隶属度确定的目标隶属度是"真值"在当前条件下的最优近似.模糊逻辑是在隶属度转换条件下对人类近似推理本领规范的一种方法.而进行规范的依据是区分权滤波的冗余理论,实质性计算是由冗余理论导出的、实现隶属度转换的非线性去冗算法;相应的隶属度转换模型是非线性数学模型. 相似文献