A general algebraic semantics for sentential logics

A general algebraic semantics for sentential logics

by Font, Josep Maria

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An exposition of the approach to the algebraization of sentential logics developed by the Barcelona logic group.

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Title Statements

  • Full title :A general algebraic semantics for sentential logics / Josep Maria Font, Ramon Jansana.

Summary

An exposition of the approach to the algebraization of sentential logics developed by the Barcelona logic group.

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Edition Statements

  • Publication Date:2017.
  • Edition:Second edition

Publication Statements

The Physical Object

  • Description:1 online resource

Edition Identifiers

  • ISBN:9781316754733, 1316754731, 9781316716915, 1316716910, 9781316748947, 1316748944, 1316752801, 9781316752807
  • oclc:ocn982287929
  • LC Classification:QA10
  • Dewey Decimal:511.3/24

Table of Contents

Cover; Half-title ; Series information ; Title page ; Copyright information ; Table of contents ; INTRODUCTION; Some history; What is a logic?; Outline of the contents; Acknowledgements; Note to the second edition (2009); CHAPTER 1 GENERALITIES ON ABSTRACT LOGICS AND SENTENTIAL LOGICS; Algebras; Formulas, equations, interpretations; Matrices; Abstract logics; Logical congruences; Bilogical morphisms and logical quotients; Sentential logics; S-filters and S-matrices; The classes Alg* S and K[sub(S)] ; CHAPTER 2 ABSTRACT LOGICS AS MODELS OF SENTENTIAL LOGICS; 2.1. Models and full models

2.2. S-algebras2.3. The lattice of full models over an algebra; 2.4. Full models and metalogical properties; The congruence property; The Property of Conjunction; The Deduction-Detachment Theorem; The Property of Disjunction; The two forms of Reductio ad Absurdum; Some rules of introduction of modality; CHAPTER 3 APPLICATIONS TO PROTOALGEBRAIC AND ALGEBRAIZABLE LOGICS; CHAPTER 4 ABSTRACT LOGICS AS MODELS OF GENTZEN SYSTEMS; 4.1. Gentzen systems and their models; 4.2. Selfextensional logics with Conjunction; 4.3. Selfextensional logics having the Deduction Theorem

CHAPTER 5 APPLICATIONS TO PARTICULA…

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Subjects

Algebraic logic Logique algébrique MATHEMATICS -- General

Writers

Font, Josep Maria Jansana, Ramón

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