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Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations - 1st Edition - ISBN: 9780081007518, 9780128045091

Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations

1st Edition

Authors: Gemma Robles José Méndez
eBook ISBN: 9780128045091
Paperback ISBN: 9780081007518
Imprint: Academic Press
Published Date: 2nd January 2018
Page Count: 158
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Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations examines how to introduce intuitionistic-type negations into RM-semantics. RM-semantics is highly malleable and capable of modeling families of logics which are very different from each other. This semantics was introduced in the early 1970s, and was devised for interpreting relevance logics. In RM-semantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De Morgan negations. This book provides research on particular features of intuitionistic-type of negations in RM-semantics, while also defining the basic systems and many of their extensions by using models with or without a set of designated points.

Key Features

  • Provides a clear development of the fundamentals of RM-semantics in a new application
  • Covers the most general research on ternary relational semantics
  • Includes scrutiny of constructive negation from the ternary relational perspective


Mathematicians and logicians interested in applications of ternary relational semantics

Table of Contents

PART I. Models with Set of Designated Points
1. The basic logic Bc and its semantics
2. Completeness of Bc
3. Extensions of Bc

PART II. Models without a Set of Designated Points
4. The logic BK
5. Extensions of BK

PART III. Formulations by Means of a Falsity Constant
6. The logics B+,F and BK+,F
7. Definitional equivalence

PART IV. Relevance and Intuitionistic-Type Negations
8. The logic RBc and its extensions
9. The logic RB+,t,F and its extensions


No. of pages:
© Academic Press 2018
2nd January 2018
Academic Press
eBook ISBN:
Paperback ISBN:

About the Authors

Gemma Robles

Gemma Robles is a researcher at the Department of Psychology, Sociology, and Philosophy at the Universidad de León. Since 2011, she has published more than 50 papers on non-classical logics in impact journals.

Affiliations and Expertise

Researcher, Department of Psychology, Sociology, and Philosophy, Universidad de León

José Méndez

José M. Méndez is a Professor of Logic at the Universidad de Salamanca. His research interests include philosophical logic focusing on modal logics, multivalued logics, and relevance logics.

Affiliations and Expertise

Professor of Logic, Universidad de Salamanca


"The authors present an overarching inquiry into modeling negation in the context of the Routley-Meyer semantics based on the idea that there is a connection between implication and negation. The book will be of interest to logicians who are interested in non-classical logics together with interpretations for these logics." --Mathematical Reviews Clippings

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