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Logic and Implication

An Introduction to the General Algebraic Study of Non-classical Logics

  • Presents an introduction to the algebraic study of non-classical logics

  • Details a powerful methodology to understand logics with implication

  • Includes many particular logics as examples for the theory

Part of the book series: Trends in Logic (TREN, volume 57)

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  • ISBN: 978-3-030-85675-5
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Hardcover Book USD 139.99
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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xxii
  2. Introduction

    • Petr Cintula, Carles Noguera
    Pages 1-14
  3. Weakly Implicative Logics

    • Petr Cintula, Carles Noguera
    Pages 15-83
  4. Completeness Properties

    • Petr Cintula, Carles Noguera
    Pages 85-149
  5. On Lattice and Residuated Connectives

    • Petr Cintula, Carles Noguera
    Pages 151-251
  6. Generalized Disjunctions

    • Petr Cintula, Carles Noguera
    Pages 253-310
  7. Semilinear Logics

    • Petr Cintula, Carles Noguera
    Pages 311-345
  8. First-Order Predicate Logics

    • Petr Cintula, Carles Noguera
    Pages 347-412
  9. Back Matter

    Pages 413-465

About this book

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions.

Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics.

The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.

Keywords

  • Non-Classical Logics
  • Algebraic Logic
  • Abstract Algebraic Logic
  • Propositional Logic
  • Predicate Logic
  • Logical Connectives
  • Completeness Theorems
  • Algebraic Semantics
  • Logical Matrices
  • Weakly Implicative Logics
  • Substructural Logics
  • Generalized Disjunctions
  • Semilinear Logics
  • First-Order Predicate Logics
  • implication and disjunction in logics
  • logics and their algebraic semantics

Authors and Affiliations

  • Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic

    Petr Cintula

  • Institute of Information Theory and Automation of the Czech Academy of Sciences, Prague, Czech Republic

    Carles Noguera

About the authors

Petr Cintula is a senior researcher at the Institute of Computer Science of the Czech Academy of Sciences. He is co-author of over 60 publications mainly on mathematical fuzzy logic and abstract algebraic logic. Furthermore, he has co-edited the three volumes of Handbook of Mathematical Fuzzy Logic and has been principal (co-)investigator of numerous research projects.

 

Carles Noguera is a senior researcher at the Institute of Information Theory and Automation of the Czech Academy of Sciences, where he has led several research projects on topics of mathematical fuzzy logic, many-valued logics, and abstract algebraic logic. He obtained his degrees in Mathematics and Philosophy and a PhD in Logic at the University of Barcelona.


Bibliographic Information

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-85675-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 139.99
Price excludes VAT (USA)