1,721,045 research outputs found
On some varieties of MTL-algebras
Full text linkThe study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this paper to the general non-involutive case, i.e. to MTL-algebras. To this end we describe the radical of MTL-algebras and characterize perfect MTL-algebras as those for which the quotient by the radical is isomorphic to the two-element Boolean algebra, and a special class of bipartite MTL-algebras, BP0, as those for which the quotient by the radical is a Boolean algebra. We prove that BP0 is the variety generated by all perfect MTL-algebras and give some equational bases for it. We also introduce a new way to build MTL-algebras by adding a negation fixpoint to a perfect algebra and also by adding some set of points whose negation is the fixpoint. Finally, we consider the varieties generated by those algebras, giving equational bases for them, and we study which of them define a fuzzy logic with standard completeness theorem. © 2005 Oxford University Press
On triangular norm based axiomatic extensions of the weak nilpotent minimum logic
Full text linkIn this paper we carry out an algebraic investigation of the weak nilpotent minimum logic (WNM) and its t-norm based axiomatic extensions. We consider the algebraic counterpart of WNM, the variety of WNM-algebras (double-struck Wdouble-struck Ndouble-struck M) and prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM-chains, in particular varieties generated by standard WNM-chains, or equivalently t-norm based axiomatic extensions of WNM, and we study their standard completeness properties. We also characterize the generic WNM-chains, i. e. those that generate the variety double-struck Wdouble-struck Ndouble-struck M, and we give finite axiomatizations for some t-norm based extensions of WNM
Perfect and bipartite IMTL-algebras and disconnected rotations of prelinear semihoops
No full textIMTL logic was introduced in [12] as a generalization of the infinitely-valued logic of Lukasiewicz, and in [11] it was proved to be the logic of left-continuous t-norms with an involutive negation and their residua. The structure of such t-norms is still not known. Nevertheless, Jenei introduced in [20] a new way to obtain rotation-invariant semigroups and, in particular, IMTL-algebras and left-continuous t-norm with an involutive negation, by means of the disconnected rotation method. In order to give an algebraic interpretation to this construction, we generalize the concepts of perfect, bipartite and local algebra used in the classification of MV-algebras to the wider variety of IMTL-algebras and we prove that perfect algebras are exactly those algebras obtained from a prelinear semihoop by Jenei's disconnected rotation. We also prove that the variety generated by all perfect IMTL-algebras is the variety of the IMTL-algebras that are bipartite by every maximal filter and we give equational axiomatizations for it. © Springer-Verlag 2005
On varieties generated by weak nilpotent minimum t-norms
Full text linkIn this paper we study Weak Nilpotent Minimum t-norms and their associated algebraic structures, the standard WNM-chains. We classify all the varieties generated by one standard WNM-chain, obtaining all the axiomatic extensions of WNM logic that are complete with respect to the semantics given by a left-continuous t-norm. To this end, we define a set of canonical standard WNM-chains and we prove that they generate pairwise different varieties and there are no other varieties generated by a standard WNM-chain
Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results
Full text linkIn this paper we study generic expansions of logics of continuous t-norms with truth-constants, taking advantage of previous results for Łukasiewicz logic and more recent results for Gödel and Product logics. Indeed, we consider algebraic semantics for expansions of logics of continuous t-norms with a set of truth-constants { over(r, -) | r ∈ C }, for a suitable countable C ⊆ [0, 1], and provide a full description of completeness results when (i) the t-norm is a finite ordinal sum of Łukasiewicz, Gödel and Product components, (ii) the set of truth-constants covers all the unit interval in the sense that each component of the t-norm contains at least one value of C different from the bounds of the component, and (iii) the truth-constants in Łukasiewicz components behave as rational numbers. © 2007 Elsevier B.V. All rights reserved
On the Standard and Rational Completeness of some Axiomatic Extensions of the Monoidal T-norm Logic
No full textThe monoidal t-norm based logic MTL is obtained from Hájek 's Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. © 2002 Kluwer Academic Publishers
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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