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.
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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
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.
José M. Méndez Professor of Logic, Universidad de Salamanca.
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.