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On BCK Algebras - Part I.a: An Attempt to Treat Unitarily the Algebras of Logic. New Algebras
No full textSince all the algebras connected to logic have, more or less explicitely, an associated order relation, it follows that they have two presentations, dual to each other. We classify these dual presentations in "left" and "right" ones and we consider that, when dealing with several algebras in the same research, it is useful to present them unitarily, either as "left" algebras or as "right" algebras. In some circumstances, this choice is essential, for instance if we want to build the ordinal sum (product) between a BL algebra and an MV algebra. We have chosen the "left" presentation and several algebras of logic have been redefined as particular cases of BCK algebras. We introduce several new properties of algebras of logic, besides those usually existing in the literature, which generate a more refined classification, depending on the properties satisfied. In this work (Parts I-V) we make an exhaustive study of these algebras - with two bounds and with one bound - and we present classes of finite examples, in bounded case. In this Part I, divided in two because of its length, after surveying chronologically several algebras related to logic, as residuated lattices, Hilbert algebras, MV algebras, divisible residuated lattices, BCK algebras, Wajsberg algebras, BL algebras, MTL algebras, WNM algebras, IMTL algebras, NM algebras, we propose a methodology in two steps for the simultaneous work with them (the first part of Part I). We then apply the methodology, redefining those algebras as particular cases of reversed left-BCK algebras. We analyse among others the properties Weak Nilpotent Minimum and Double Negation of a bounded BCK(P) lattice, we introduce new corresponding algebras and we establish hierarchies (the subsequent part of Part I)
On the construction of three-valued Lukasiewicz-Moisil algebras
No full textAbstractThe author constructs a three-valued Lukasiewicz-Moisil algebra from a monadic three-valued Lukasiewicz-Moisil algebra, generalizing A. Monteiro's (1974) construction of a three-valued Lukasiewicz-Moisil algebra from a monadic Boolean algebra, and constructs a monadic three-valued Lukasiewicz-Moisil algebra from a monadic n-valued one, generalizing V. Boicescu's (1971) construction of a three-valued Lukasiewicz-Moisil algebra from an n-valued one, n ⩾ 3. Thus one can construct a three-valued Lukasiewicz-Moisil algebra from a monadic n-valued Lukasiewicz-Moisil algebra, n ⩾ 2
Connections between MVn algebras and n-valued Lukasiewicz-Moisil algebras Part I
No full textAbstractI introduce in the MVn algebras of Revaz Grigolia two chains of unary operations, which are key in establishing many connections between these algebras and n-valued Lukasiewicz-Moisil algebras (LMn algebras for short). The study has three parts. It is self-contained as much as possible.The main result of the first part is that MV4 algebras coincide with LM4 algebras. The larger class of ‘relaxed’-MVn algebras is also introduced and studied. This class is related to the class of generalized LMn pre-algebras.The main result of the second part is that, for n ⩾ 5, any MVn algebra is an LMn algebra and the converse is not true.The main result of the third part is the construction of an LM3(LM4) algebra from the odd (even)-valued LMn algebra (n ⩾ 5). This proves that LM4 algebras are as important as LM3 algebras; MVn algebras helped us to see that
L-prealgebras
No full textAbstractWe introduce the notion of S-prealgebra and give a theorem from which Theorems 6.5, 9.2 and a generalization of 13.10 from Chapter VIII of H. Rasiowa's An Approach to Non-classical Logics follow as corollaries
Functors between categories of three-valued Lukasiewicz-Moisil algebras I
No full textAbstractWe prove that if L is a given three-valued Lukasiewicz-Moisil algebra, then there exists a monadic three-valued Lukasiewicz-Moisil algebra A, such that L is isomorphic with a certain subalgebra of the three-valued Lukasiewicz-Moisil algebra L(A)
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Get PDF“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
Get PDFWe 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
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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