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1.
《International Journal of Approximate Reasoning》2014,55(5):1164-1184
An integrated approach to truth-gaps and epistemic uncertainty is described, based on probability distributions defined over a set of three-valued truth models. This combines the explicit representation of borderline cases with both semantic and stochastic uncertainty, in order to define measures of subjective belief in vague propositions. Within this framework we investigate bridges between probability theory and fuzziness in a propositional logic setting. In particular, when the underlying truth model is from Kleene's three-valued logic then we provide a complete characterisation of compositional min–max fuzzy truth degrees. For classical and supervaluationist truth models we find partial bridges, with min and max combination rules only recoverable on a fragment of the language. Across all of these different types of truth valuations, min–max operators are resultant in those cases in which there is only uncertainty about the relative sharpness or vagueness of the interpretation of the language. 相似文献
2.
设M是一个MV-代数,Ω是从MV-代数M到MV-单位区间的全体赋值之集,μ是Ω上的概率测度.本文基于μ在M中引入了元素的尺寸和元素对之间的相似度概念,并由此在M上建立了度量结构.给出了MV-代数上的度量结构在多值逻辑中的一些应用. 相似文献
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A. A. Esin 《Mathematical Notes》2008,83(5-6):594-603
A classical theorem of Post [1] describes five precomplete classes in the set of Boolean functions. In [2], it was shown that there exist 18 precomplete classes of functions of three-valued logic. In [1, 2], the closure of sets of functions with respect to the substitution operator was studied. We consider two closure operators on functions of three-valued logic, which are obtained by supplementing the substitution operator by closures with respect to two identifications of function values, and prove the existence of three precomplete classes for one of these operators and five precomplete classes for the other. 相似文献
6.
经典命题逻辑的Boole语义理论 总被引:3,自引:2,他引:1
以有限Boole代数作为赋值域建立了经典命题逻辑的一种新的语义理论;证明了命题逻辑公式为重言式当且仅当该命题的每个赋值都等于Boole代数的最大元;在这种新语义理论中提出了公式的B-度实概念,研究了B-真度的基本性质。 相似文献
7.
本文推广第二作者建立色觉机制数学模型时发明的一种连续值逻辑方法-模糊开关准布尔代数,得到了线面体混合布尔函数-若干个互不相交的子区域-边界的求解方法;这种方法用布尔代数公式和max、min运算代替复杂的条件判断,具有可靠性、通用性和简洁性。 相似文献
8.
In this paper, we study some kinds of generalized valuations on MTL-algebras, discuss the relationship between the cokernel of generalized valuations and types of filters on MTL-algebras. Then, we give some equivalent characterizations of positive implicative generalized valuations on MTL-algebras. Finally, we characterize the structure theory of quotient MTL algebras based on the congruence relation, which is constructed by generalized valuations. The results of this paper not only generalize related theories of generalized valuations, but also enrich the algebraic conclusion of probability measure, on algebras of triangular norm based fuzzy logic. 相似文献
9.
三值R_0命题逻辑系统中理论的随机发散度 总被引:3,自引:0,他引:3
在三值R_0命题逻辑系统中,给出了随机相似度和随机逻辑伪距离的基本性质.然后在随机逻辑度量空间中提出了理论的随机发散度,指出全体原子公式之集在随机逻辑度量空间中未必是全发散的,其是否全发散取决于给定的随机数序的分布. 相似文献
10.
D. A. Dagaev 《Moscow University Mathematics Bulletin》2011,66(3):133-135
The problem of the realization complexity for functions of the three-valued logic taking values from the set {0, 1} by formulas
over incomplete generating systems is considered. Upper and lower asymptotic estimates for the corresponding Shannon functions
are obtained. 相似文献
11.
A bipolar model of assertability and belief 总被引:1,自引:0,他引:1
Jonathan Lawry Inés González-Rodríguez 《International Journal of Approximate Reasoning》2011,52(1):76-91
Valuation pairs are introduced as a bipolar model of the assertability of propositions. These correspond to a pair of dual valuation functions, respectively, representing the strong property of definite assertability and the dual weaker property of acceptable assertability. In the case where there is uncertainty about the correct valuation pair for a language then a probability distribution is defined on possible valuation pairs. This results in two measures, μ+ giving the probability that a sentence is definitely assertable, and μ− giving the probability that a sentence is acceptable to assert. It is shown that μ+ and μ− can be determined directly from a two dimensional mass function m defined on pairs of sets of propositional variables. Certain natural properties of μ+ and μ− are easily expressed in terms of m, and in particular we introduce certain consonance or nestedness assumptions. These capture qualitative information in the form of assertability orderings for both the propositional variables and the negated propositional variables. On the basis of these consonance assumptions we show that label semantics, intuitionistic fuzzy logic and max-min fuzzy logic can all be viewed as special cases of this bipolar model. We also show that bipolar belief measures can be interpreted within an interval-set model. 相似文献
12.
Steven Vickers 《Mathematical Logic Quarterly》2008,54(1):109-123
An account of lower and upper integration is given. It is constructive in the sense of geometric logic. If the integrand takes its values in the non‐negative lower reals, then its lower integral with respect to a valuation is a lower real. If the integrand takes its values in the non‐negative upper reals, then its upper integral with respect to a covaluation and with domain of integration bounded by a compact subspace is an upper real. Spaces of valuations and of covaluations are defined. Riemann and Choquet integrals can be calculated in terms of these lower and upper integrals. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
Zeng Guangxing 《代数通讯》2013,41(10):3052-3063
The purpose of this article is to introduce the notion of real valuations on modules over commutative rings. These real valuations are characterized by their associated valuation triples, and a necessary and sufficient condition for a module to possess a real valuation is established. Moreover, the close interplay between valuations and orderings on a module is investigated by introducing the compatibility of valuations with orderings. Via the compatibility of valuations with orderings, the reality of valuations on a module also is characterized. 相似文献
14.
Nic Wilson 《Journal of Heuristics》2006,12(4-5):241-262
Representing and reasoning with an agent’s preferences is important in many applications of constraints formalisms. Such preferences
are often only partially ordered. One class of soft constraints formalisms, semiring-based CSPs, allows a partially ordered
set of preference degrees, but this set must form a distributive lattice; whilst this is convenient computationally, it considerably
restricts the representational power. This paper constructs a logic of soft constraints where it is only assumed that the
set of preference degrees is a partially ordered set, with a maximum element 1 and a minimum element 0. When the partially
ordered set is a distributive lattice, this reduces to the idempotent semiring-based CSP approach, and the lattice operations
can be used to define a sound and complete proof theory. A generalised possibilistic logic, based on partially ordered values
of possibility, is also constructed, and shown to be formally very strongly related to the logic of soft constraints. It is
shown how the machinery that exists for the distributive lattice case can be used to perform sound and complete deduction,
using a compact embedding of the partially ordered set in a distributive lattice. 相似文献
15.
S. S. Marchenkov 《Journal of Applied and Industrial Mathematics》2014,8(2):256-266
We state some theoretical prerequisites and indicate approaches to constructing a positive classification of the set of functions of k-valued logic. Basing on this, we find all 194 positively closed classes of three-valued logic. We describe them using the semigroups of endomorphisms and indicating positive bases. 相似文献
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Pilar Dellunde Lluís Godo Enrico Marchioni 《International Journal of Approximate Reasoning》2011,52(1):63-75
In this paper we present several fuzzy logics trying to capture different notions of necessity (in the sense of possibility theory) for Gödel logic formulas. Based on different characterizations of necessity measures on fuzzy sets, a group of logics with Kripke style semantics is built over a restricted language, namely, a two-level language composed of non-modal and modal formulas, the latter, moreover, not allowing for nested applications of the modal operator N. Completeness and some computational complexity results are shown. 相似文献
17.
Using a linear programming model for the financial planning of an organization requires the specification of a horizon date and a valuation of the firm at that date. Given perfect information about future opportunities, an exact valuation procedure should lead to the same optimal solution of the model regardless of the choice of horizon date. Even in the absence of perfect information, conventional valuations fall far shorter of this ideal than they need to. It is shown that for a modest increase in the size of the linear programme, better valuations can be achieved and, most importantly, valuations which consider the impact on the value of the firm of post horizon constraints and liabilities as well as post-horizon opportunities. 相似文献
18.
I. D. Zaslavsky 《Journal of Mathematical Sciences》2005,130(2):4578-4597
Formal axiomatic theories based on the three-valued logic of Lukasiewicz are considered. Main notions related to these theories, in particular, those of Luk-model, Luk-consistent theory, and Luk-complete theory are introduced. Logical calculuses that describe such theories are defined; counterparts of the classical compactness and completeness theorems are proved. Theories of arithmetic based on Lukasiewicz’s logic and on its constructive (intuitionistic) variant are investigated; the theorem on effective Luk-incompleteness is proved for a large class of arithmetic systems. This theorem is a three-valued counterpart of the famous Godel theorem on incompleteness of formal theories. Three-valued counterparts of Presburger’s arithmetic system are defined and proved to be Luk-complete but incomplete in the classical sense. Bibliography: 29 titles.__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 304, 2002, pp. 19–74. 相似文献
19.
The theory of valuations on fields is developed in the constructive spirit of Errett Bishop. As a consequence of the general theory we are able to construct all nonarchimedean valuations on algebraic number fields and compute their ramification indices and residue class degrees. The notion of a field with a valuation for which the infimum of the values of any polynomial function can be computed plays an important role. Numerous limiting counterexamples are provided. 相似文献
20.
The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of
fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises
weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability
of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style
completeness theorem (degree of provability equals degree of truth) from which we get some particular cases by imposing restrictions
on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic. 相似文献