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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.
- 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
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
- 9th January 2018
- Academic Press
- Paperback ISBN:
- eBook ISBN:
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.
Researcher, Department of Psychology, Sociology, and Philosophy, Universidad de León
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.
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