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Lògiques distributives i booleanes.

Ventura Verdú i Solans (1979)

Stochastica

Continuing the study of different types of Abstract Logics [5], and following works by Brown-Bloom [1] and Brown-Suszko [2], we analyze in this paper some logics in which, if we identify equivalent formulae by means of the consequence operator, we obtain distributive lattices or Boolean algebras.

M V -test spaces versus M V -algebras

Antonio Di Nola, Anatolij Dvurečenskij (2004)

Czechoslovak Mathematical Journal

In analogy with effect algebras, we introduce the test spaces and M V -test spaces. A test corresponds to a hypothesis on the propositional system, or, equivalently, to a partition of unity. We show that there is a close correspondence between M V -algebras and M V -test spaces.

Many-sorted coalgebraic modal logic : a model-theoretic study

Bart Jacobs (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

This paper gives a semantical underpinning for a many-sorted modal logic associated with certain dynamical systems, like transition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial functors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many-sorted Boolean Algebras with...

Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study

Bart Jacobs (2010)

RAIRO - Theoretical Informatics and Applications

This paper gives a semantical underpinning for a many-sorted modal logic associated with certain dynamical systems, like transition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial functors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many-sorted Boolean Algebras with...

Matrix of ℤ-module1

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2015)

Formalized Mathematics

In this article, we formalize a matrix of ℤ-module and its properties. Specially, we formalize a matrix of a linear transformation of ℤ-module, a bilinear form and a matrix of the bilinear form (Gramian matrix). We formally prove that for a finite-rank free ℤ-module V, determinant of its Gramian matrix is constant regardless of selection of its basis. ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattices [22]...

Metric similarities in the logic of approximation.

Michael Katz (1982)

Stochastica

We describe restricted and extended versions of the logic of approximation which is meant to handle formally the problems of measurement error and of deduction under conditions of uncertainty. We apply the logic to the foundations of social and behavioral inquiry, axiomatizing in it an inexact similarity predicate which behaves like a metric approximation to identity. In the restricted version of the logic we formulate conditions for the imbeddability of similarity models in the real line, and in...

Migrativity properties of 2-uninorms over semi-t-operators

Ying Li-Jun, Qin Feng (2022)

Kybernetika

In this paper, we analyze and characterize all solutions about α -migrativity properties of the five subclasses of 2-uninorms, i. e. C k , C k 0 , C k 1 , C 1 0 , C 0 1 , over semi-t-operators. We give the sufficient and necessary conditions that make these α -migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for G ∈ C k , the α -migrativity of G over a semi-t-operator F μ , ν is closely related to the α -section of F μ , ν or the ordinal sum representation of t-norm...

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