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E-raamat: Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations

(Professor of Logic, Universidad de Salamanca), (Researcher, Department of Psychology, Sociology, and Philosophy, Universidad de León)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 02-Jan-2018
  • Kirjastus: Academic Press Inc.(London) Ltd
  • Keel: eng
  • ISBN-13: 9780128045091
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Routley-Meyer Ternary Relational Semantics for Intuitionistic-type NegationsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 02-Jan-2018
  • Kirjastus: Academic Press Inc.(London) Ltd
  • Keel: eng
  • ISBN-13: 9780128045091
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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

Arvustused

"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

About the authors vii
Preface ix
Introduction xi
0.1 Ternary relational semantics. General characteristics xi
0.2 Positive models. The interpretation of the conditional xii
0.3 The interpretation of negation in RM-semantics xvi
0.4 The introduction of intuitionistic-type negation in standard positive binary semantics xvii
0.5 The introduction of intuitionistic-type negation in RM-semantics xix
Part 1
1 The basic positive logic B+.EB+-models
3(18)
1.1 EB+-models
3(4)
1.2 The logic B+
7(2)
1.3 Completeness of EB+-logics I. Basic propositions and lemmas
9(6)
1.4 Completeness of EB+-logics II. Canonical models, Completeness of B+
15(2)
1.5 "Rules of inference", "rules of proof", and strong completeness
17(4)
2 The basic constructive logics Bcs and Bc
21(7)
2.1 The logic BcS
21(3)
2.2 An RM-semantics for BcS
24(2)
2.3 Completeness of BC5 I. On w-consistency
26(2)
24 Completeness of Bcs II. The canonical model. The completeness theorem
28(11)
2.5 The logic Bc
32(3)
2.6 BcS and Bc as the basic constructive logics in RM1-semantics
35(4)
3 The basic positive logic Br+. The basic constructive logics BKS and BK
39(14)
3.1 The logic BK+ and its semantics
39(4)
3.2 Completeness of Bk+
43(2)
3.3 The logic BKS
45(3)
3.4 The logic BK
48(5)
Part 2
4 Logics definitionally equivalent to the basic constructive logics The logics BcSf, Bcf, BKsf, and BKf
53(10)
4.1 The logics B+,f and BK+f
53(2)
4.2 The logics BcSf-, Bcf, BKSf-, and BKf
55(1)
4.3 Definitional equivalence
56(3)
4.4 RM-semantics for the basic constructive f-logics
59(4)
5 The basic constructive logics RBc and RBc2
63(12)
5.1 The logic RBc
63(3)
5.2 The logic RBc2
66(5)
5.3 The logic RB+, t,f
71(1)
5.4 Independence and variable-sharing property in RBc and RBc2
72(3)
6 Extensions and expansions of the basic logics
75(34)
6.1 Extensions and expansions with positive axioms
75(13)
6.2 Extensions and expansions with negation axioms
88(8)
6.3 Extensions and expansions with ∫-axioms
96(13)
7 On some extensions and expansions of the basic logics
109(10)
7.1 Some systems definable from t1-t71
109(3)
7.2 No collapse between certain systems
112(4)
7.3 Relevance and paraconsistent logics
116(3)
A List of axioms and postulates
119(10)
A.1 Positive and negation axioms and their corresponding postulates
119(4)
A.2 ∫-axioms and their corresponding ∫-postulates
123(6)
Bibliography 129(4)
Index 133
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 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.
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