Beziau Logica Universalis

Towards a General Theory of Logic
2. Auflage 2007
ISBN: 978-3-7643-8354-1
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 246 Seiten

Autoren/Hrsg.

Beziau, Jean-Yves

Inhaltsverzeichnis

1;Contents;5
2;Preface;7
2.1;References;10
3;Preface to the Second Edition;11
4;From Consequence Operator to Universal Logic: A Survey of General Abstract Logic;13
4.1;1. Introduction;13
4.2;2. Tarski’s consequence operator;14
4.3;3. Hertz and Gentzen’s proof systems;16
4.4;4. Matrix theory and abstract logic;19
4.5;5. Algebraic logic;20
4.6;6. Da Costa’s theory of valuation;22
4.7;7. Universal logic;23
4.8;References;25
5;Abstract Model Theory as a Framework for Universal Logic;28
5.1;1. Introduction;28
5.2;2. Abstract Model Theory;29
5.3;3. Lindstr¨ om Theorems;34
5.4;4. Abstract logic without negation;37
5.5;5. Logic frames;38
5.6;References;40
6;A Topological Approach to Universal Logic: Model- Theoretical Abstract Logics;43
6.1;1. Introduction;43
6.2;2. Model-theoretical abstract logics;45
6.3;3. Two examples;67
6.4;4. Future work;68
6.5;References;69
7;Selfextensional Logics with Implication;70
7.1;1. Introduction;70
7.2;2. Preliminaries;73
7.3;3. Hilbert-based deductive systems;77
7.4;4. Fregean logics with a deduction-detachment theorem;83
7.5;5. Selfextensional logics with a deduction-detachment theorem and Gentzen calculi;86
7.6;References;92
8;Logic without Self-Deductibility;94
8.1;1. The law of self-deductibility;94
8.2;2. A model for a logic without self-deductibility;95
8.3;3. Category-theoretic aspects of the subject;97
8.4;References;100
9;Equipollent Logical Systems;102
9.1;1. Introduction;102
9.2;2. From logical systems to theory spaces;104
9.3;3. Isomorphisms;106
9.4;4. Equipollence;110
9.5;5. Conclusion;113
9.6;References;114
10;What is a Logic?;115
10.1;1. Introduction;115
10.2;2. Institutions and Logics;117
10.3;3. Equivalence of Institutions;120
10.4;4. Model-Theoretic Invariants of Institutions;123
10.5;5. Proof Theoretic Invariants;127
10.6;6.;132
10.7;institutions;132
10.8;7. Conclusions;134
10.9;References;135
11;What is a Logic, and What is a Proof ?;138
11.1;1. Introduction;138
11.2;2. What is a logic ?;139
11.3;3. What is a proof ?;143
11.4;4. Summary;152
11.5;References;153
12;Non-deterministic Matrices and Modular Semantics of Rules;157
12.1;1. Introduction;157
12.2;2. Preliminaries;158
12.3;3. Semantics for the Basic System;164
12.4;4. Semantics for the Extensions of B Induced by;167
12.5;5. Applications;169
12.6;6. Other Plausible Extensions of the Basic System;170
12.7;7. Conclusions and Further Research;173
12.8;References;174
13;Two’s Company: The Humbug of Many Logical Values”;176
13.1;1. Suszko’s Thesis;177
13.2;2. Reductive results;178
13.3;3. Separating truth-values;180
13.4;4. Dyadic semantics;183
13.5;5. From finite matrices to dyadic valuations;185
13.6;6. Some Illustrations;187
13.7;7. Application: tableaux for logics with dyadic semantics;191
13.8;8. Conclusions;193
13.9;References;194
14;Friendliness and Sympathy in Logic†;196
14.1;1. Friendliness;196
14.2;2. Links with Familiar Notions;207
14.3;3. From Friendliness to Sympathy;215
14.4;4. Open Questions;221
14.5;5. Appendix;222
14.6;References;224
15;Logical Discrimination;226
15.1;1. Introduction;226
15.2;2. Discrimination In Logics as Sets of Formulas;230
15.3;3. Discrimination in Logics as Consequence Relations;236
15.4;References;245