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Aggregate theory versus set theory

Hartley Slater (2005)

Philosophia Scientiae

Les arguments de Maddy avancés en 1990 contre la théorie des agrégats se trouvent affaiblis par le retournement qu’elle opère en 1997. La présente communication examine cette théorie à la lumière de ce retournement ainsi que des récentes recherches sur les “Nouveaux axiomes pour les mathématiques”. Si la théorie des ensembles est la théorie de la partie–tout des singletons, identifier les singletons à leurs membres singuliers ramène la théorie des ensembles à la théorie des agrégats. Toutefois si...

Aggregation of fuzzy vector spaces

Carlos Bejines (2023)

Kybernetika

This paper contributes to the ongoing investigation of aggregating algebraic structures, with a particular focus on the aggregation of fuzzy vector spaces. The article is structured into three distinct parts, each addressing a specific aspect of the aggregation process. The first part of the paper explores the self-aggregation of fuzzy vector subspaces. It delves into the intricacies of combining and consolidating fuzzy vector subspaces to obtain a coherent and comprehensive outcome. The second...

Aggregation operators and fuzzy measures on hypographs

Doretta Vivona, Maria Divari (2002)

Kybernetika

In a fuzzy measure space we study aggregation operators by means of the hypographs of the measurable functions. We extend the fuzzy measures associated to these operators to more general fuzzy measures and we study their properties.

Aggregation operators from the ancient NC and EM point of view

Ana Pradera, Enric Trillas (2006)

Kybernetika

This paper deals with the satisfaction of the well-known Non-Contradiction (NC) and Excluded-Middle (EM) principles within the framework of aggregation operators. Both principles are interpreted in a non-standard way, based on self-contradiction (as in Ancient Logic) instead of falsity (as in Modern Logic). The logical negation is represented by means of strong negation functions, and conditions are given both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given...

Aggregation operators on partially ordered sets and their categorical foundations

Mustafa Demirci (2006)

Kybernetika

In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of L -fuzzy set-theoretic notions and their justification. In order to solve these problems, we will formulate aggregation operators and their special types on partially ordered sets with universal bounds, and introduce their categories. Furthermore, we will show that there exists a strong connection between the category of aggregation operators...

Aggregations preserving classes of fuzzy relations

Józef Drewniak, Urszula Dudziak (2005)

Kybernetika

We consider aggregations of fuzzy relations using means in [0,1] (especially: minimum, maximum and quasilinear mean). After recalling fundamental properties of fuzzy relations we examine means, which preserve reflexivity, symmetry, connectedness and transitivity of fuzzy relations. Conversely, some properties of aggregated relations can be inferred from properties of aggregation results. Results of the paper are completed by suitable examples and counter- examples, which is summarized in a special...

Alcune osservazioni sul linguaggio L ⁢ ( Q 1 )

Aroldo Goretti (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An existence theorem for 1-atomic standard models of L ω ⁢ ω ⁢ ( Q 1 ) (more weak than usual “atomic models”) and applications of L ω ⁢ ω ⁢ ( Q 1 ) to L ω ⁢ ω are the results of this note.

Alcune proprietà delle algebre di Boole principali

Francesco Lacava (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper some properties of principal Boolean algebras are studied.

Aleatoreidad e inmunidad.

J. F. Prida (1995)

Revista Matemática de la Universidad Complutense de Madrid

By introducing the concept of randomness through notions of recursion theory, the set of the random numbers is effectively immune. The proof of this well-known result makes an essential use of the recursion theorem. In this paper, randomness is introduced starting from the more common notion of definability in Robinson's arithmetic and the same result is obtained using an extension of the fixed-point theorem, which we prove at the end of the paper. Finally we define a recursive function dominating...

Algebra grammars

Radim Bělohlávek (1995)

Acta Mathematica et Informatica Universitatis Ostraviensis

Algebra of Polynomially Bounded Sequences and Negligible Functions

Hiroyuki Okazaki (2015)

Formalized Mathematics

In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation between polynomially...

Algebraic Approach to Algorithmic Logic

Grzegorz Bancerek (2014)

Formalized Mathematics

We introduce algorithmic logic - an algebraic approach according to [25]. It is done in three stages: propositional calculus, quantifier calculus with equality, and finally proper algorithmic logic. For each stage appropriate signature and theory are defined. Propositional calculus and quantifier calculus with equality are explored according to [24]. A language is introduced with language signature including free variables, substitution, and equality. Algorithmic logic requires a bialgebra structure...

Algebraic approximation of analytic sets definable in an o-minimal structure

Marcin Bilski, Kamil Rusek (2010)

Annales Polonici Mathematici

Let K,R be an algebraically closed field (of characteristic zero) and a real closed field respectively with K=R(√(-1)). We show that every K-analytic set definable in an o-minimal expansion of R can be locally approximated by a sequence of K-Nash sets.

Algebraic axiomatization of tense intuitionistic logic

Ivan Chajda (2011)

Open Mathematics

We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction of these tense operators on complete relatively pseudocomplemented lattice which is a...

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