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Algebra universalis - We prove an algebraic result concerning inverse limits of copowers in anS-class of relational structures of the same (finitary or infinitary) type. Among several applications... 相似文献
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While every finite lattice-based algebra is dualisable, the same is not true of semilattice-based algebras. We show that a
finite semilattice-based algebra is dualisable if all its operations are compatible with the semilattice operation. We also
give examples of infinite semilattice-based algebras that are dualisable. In contrast, we present a general condition that
guarantees the inherent non-dualisability of a finite semilattice-based algebra. We combine our results to characterise dualisability
amongst the finite algebras in the classes of flat extensions of partial algebras and closure semilattices. Throughout, we
emphasise the connection between the dualisability of an algebra and the residual character of the variety it generates.
Presented by R. Willard. 相似文献
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BL-algebras are the Lindenbaum algebras for Hájek's Basic Logic, just as Boolean algebras correspond to the classical propositional
calculus. The finite totally ordered BL-algebras are ordinal sums of MV-chains. We develop a natural duality, in the sense
of Davey and Werner, for each subvariety generated by a finite BL-chain, and we use it to describe the injective and the weak
injective members of these classes.
The preliminary research for this paper was carried out while the second author was visiting Salerno University. The second
author would like to thank the first author and Salerno University for their hospitality. The second author acknowledges partial
supports from Salerno University and from the belgian Fonds National de la Recherche Scientifique. 相似文献
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Flaviu Pop 《Central European Journal of Mathematics》2011,9(5):1088-1099
In this paper we consider a pair of right adjoint contravariant functors between abelian categories and describe a family of dualities induced by them. 相似文献
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This paper studies the connections between relational probabilistic models and reference classes, with specific focus on the ability of these models to generate the correct answers to probabilistic queries. We distinguish between relational models that represent only observed relations and those which additionally represent latent properties of individuals. We show how both types of relational models can be understood in terms of reference classes, and that learning such models correspond to different ways of identifying reference classes. Rather than examining the impact of philosophical issues associated with reference classes on relational learning, we directly assess whether relational models can represent the correct probabilities of a simple generative process for relational data. We show that models with only observed properties and relations can only represent the correct probabilities under restrictive conditions, whilst models that also represent latent properties avoids such restrictions. As such, methods for acquiring latent-property models are an attractive alternatives to traditional ways of identifying reference classes. Our experiments on synthetic as well as real-world domains support the analysis, demonstrating that models with latent relations are significantly more accurate than those without latent relations. 相似文献
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Alexandr Kazda 《Algebra Universalis》2016,75(1):75-84
We prove that whenever \({\mathbb {A}}\) is a 3-conservative relational structure with only binary and unary relations, then the algebra of polymorphisms of \({\mathbb {A}}\) either has no Taylor operation (i.e., CSP(\({\mathbb {A}}\)) is NP-complete), or it generates an SD(\({\wedge}\)) variety (i.e., CSP(\({\mathbb {A}}\)) has bounded width). 相似文献
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We prove that for finite, finitely related algebras, the concepts of an absorbing subuniverse and a J´onsson absorbing subuniverse coincide. Consequently, it is decidable whether a given subset is an absorbing subuniverse of the polymorphism algebra of a given relational structure. 相似文献
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Christian Delhommé 《Discrete Mathematics》2009,309(6):1374-1384
The age of a relational structure A of signature μ is the set age(A) of its finite induced substructures, considered up to isomorphism. This is an ideal in the poset Ωμ consisting of finite structures of signature μ and ordered by embeddability. We shall show that if the structures have infinitely many relations and if, among those, infinitely many are at least binary then there are ideals which do not come from an age. We provide many examples. We particularly look at metric spaces and offer several problems. We also answer a question due to Cusin and Pabion [R. Cusin, J.F. Pabion, Une généralisation de l’âge des relations, C. R. Acad. Sci. Paris, Sér. A-B 270 (1970) A17-A20]: there is an ideal I of isomorphism types of at most countable structures whose signature consists of a single ternary relation symbol such that I does not come from the set of isomorphism types of substructures of A induced on the members of an ideal I of sets. 相似文献
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Ronald Fagin 《Discrete Mathematics》1977,19(1):17-21
An elementary proof is presented of an asymptotic estimate for the number (up to isomorphism) of finite relational structures, under a quite general definition of “relational structure”. 相似文献
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Pierre Antoine Grillet 《Algebra Universalis》2005,53(4):491-503
A natural class of universal algebras is a class which is closed under isomorphism, subalgebras, disjoint suprema, and essential extensions. In suitable varieties, natural classes form a boolean lattice, and lead to a decomposition of any universal algebra into continuous molecular, discrete, and bottomless subalgebras.Dedicated to Professor John DaunsReceived March 29, 2004; accepted in final form May 20, 2004 相似文献
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Leonardo Manuel Cabrer Sergio Arturo Celani 《Central European Journal of Mathematics》2006,4(4):600-623
In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated
Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality
given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the
equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.
The authors are supported by the Agentinian Consejo de Investigaciones Cientificas y Tecnicas (CONICET). 相似文献
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Robert A. Wolak 《Geometriae Dedicata》1987,24(2):207-220
The aim of this paper is to present a basic theory of characteristic classes of almost-flag structures. Vanishing theorems for primary characteristic classes of almost-flag and almost-product structures are proved. Consequences of these theorems for secondary characteristic classes are drawn in the framework of Lehmann's theory. Two theorems on residues of flag structures complete the paper. 相似文献