Algebraic logic for classical conjunction and disjunction
type: Item
instance of: scholarly article
title: Algebraic logic for classical conjunction and disjunction
zbMATH Open document ID: 0753.03027
DOI: 10.1007/BF00370680
author: Ventura Verdú
author: Josep Maria Font
published in: Studia Logica
publication date: 1992-09-27T00:00:00Z
review text: Relationships between the fragment \(\mathbb{L}\) of classical propositional logic and the variety \(\mathbb{D}\) of distributive lattices are studied from a non-traditional point of view. They are shown to be satisfactorily covered neither by Blok and Pigozzi's algebraizable logics approach nor by use of logical matrices. To make up for the deficiency, the authors introduce a new notion of a model of a sequential calculus \(\mathcal L\) for \(\mathbb{L}\). They find that abstract logics in the sense of Suszko provide a natural tool to convert a distributive lattice into a model of \(\mathcal L\); the specified presentation of \(\mathcal L\) plays here a crucial role. The various results obtained in this paper serve as a basis for a statement that distributive lattices are the right models of \(\mathcal L\).
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 03G10
Mathematics Subject Classification ID: 03B20
Mathematics Subject Classification ID: 06B20
Mathematics Subject Classification ID: 06D05
zbMATH DE Number: 58408
zbMATH Keywords: fragment of classical propositional logic
zbMATH Keywords: variety of distributive lattices
zbMATH Keywords: algebraizable logics
zbMATH Keywords: logical matrices
zbMATH Keywords: model of a sequential calculus
zbMATH Keywords: abstract logics
MaRDI profile type: Publication
cites work: Q4083730
cites work: Q3858244
cites work: Alfred Tarski's work on general metamathematics
cites work: Algebraizable logics
cites work: Q4011710
cites work: Introduction to the special issue on algebraic logic
cites work: Continuous dependence on initial geometry for a class of abstract equations in Hilbert space
cites work: Q4078023
cites work: Key notions of Tarski's methodology of deductive systems
cites work: Q3874168
cites work: Q3041195
cites work: Q4052071
cites work: A first approach to abstract modal logics
cites work: Q3830999
cites work: Linear logic
cites work: Q3268305
cites work: Q3325691
cites work: 2-element matrices
cites work: Q4342088
cites work: Q4342086
cites work: Q3791124
cites work: Theory of logical calculi. Basic theory of consequence operations
full work available at URL: https://doi.org/10.1007/bf00370680
OpenAlex ID: W4231562412
description: scientific article; zbMATH DE number 58408