Algebra of Proofs

Name: Algebra of Proofs
Brand: Elsevier
Price: 215.0 EUR
Availability: OnlineOnly

M. E. Szabo Lev D. Beklemishev(Autor*in)

Elsevier (Verlag)

Erschienen am 14. Mai 2014

311 Seiten

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978-0-08-095497-4 (ISBN)

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Inhalt

Front Cover
Algebra of Proofs
Copyright Page
Contents
Preface
Chapter 1. Introduction
1.1 Categorical preliminaries
1.2 Logical preliminaries
Chapter 2. Monoidal Categories
2.1 Definition
2.2 Examples
2.3 The category Fm(?)
2.4 The deductive system m?(?)
2.5 The semantics of Der(m?(?))
2.6 The syntax of Fm(?)
Chapter 3. Symmetric Monoidal Categories
3.1 Definition
3.2 Examples
3.3 The category Fsm(?)
3.4 The deductive system sm?(?)
3.5 The semantics of Der(sm?(?))
3.6 The syntax of Fsm(?)
Chapter 4. Cartesian Categories
4.1 Definition
4.2 Examples
4.3 The category Fc(X)
4.4 The deductive system c?(X)
4.5 The semantics of Der(c?(X))
4.6 The syntax of Fc?(X)
Chapter 5. Bicartesian Categories
5.1 Definition
5.2 Examples
5.3 The category Fbc(X)
5.4 The deductive system bc?(X)
5.5 The semantics of Der(bc?(X))
5.6 The syntax of Fbc(X)
Chapter 6. Distributive Bicartesian Categories
6.1 Definition
6.2 Examples
6.3 The category Fdbc(X)
6.4 The deductive system dbc?(X)
6.5 The semantics of Der(dbc?(X))
6.6 The syntax of Fdbc(X)
Chapter 7. Monoidal Closed Categories
7.1 Definition
7.2 Examples
7.3 The category Fmcl(X)
7.4 The deductive system mcl?(X)
7.5 The semantics of Der(mcl?(X))
7.6 The syntax of Fmcl(X)
Chapter 8. Symmetric Monoidal Closed Categories
8.1 Definition
8.2 Examples
8.3 The category Fsmcl(X)
8.4 The deductive system smcl?(X)
8.5 The semantics of Der(smcl?(X))
8.6 The syntax of Fsmcl(X)
Chapter 9. Cartesian Closed Categories
9.1 Definition
9.2 Examples
9.3 The category Fccl(X)
9.4 The deductive system ccl?(X)
9.5 The semantics of Der(ccl?(X))
9.6 The syntax of Fccl(X)
Chapter 10. Bicartesian Closed Categories
10.1 Definition
10.2 Examples
10.3 The category Fbccl(X)
10.4 The deductive system bccl?(X)
10.5 The semantics of Der(bccl?(X))
10.6 The syntax of Fbccl(X)
Chapter 12. Monoidal Biclosed Categories
12.1 Definition
12.2 Examples
12.3 The category Fmbcl(X)
12.4 The deductive system mbcl?(X)
12.5 The semantics of Der(mbcl?(X))
12.6 The syntax of Fmbcl(X)
Chapter 13. Quantifier-Complete Categories
13.1 Categorical preliminaries
13.2 The language L*(X)
13.3 The deductive system ?*(X)
13.4 The semantics of Der(?*(X))
13.5 The syntax of Fqc(At L*(X))
Appendix A . The Labelled Deductive System b(X)
A.1 The class Lb(?X))
A.2 The axioms of ?(X)
A.3 The rules of inference of ?(X)
A.4 The class Der(?(X))
Appendix B . The Unlabelled Deductive System A(X)
B.1 The axioms of ?(X)
B.2 The rules of inference of ?(X)
B.3 The class Der(?(X))
Appendix C. The Cut Elimination Algorithm
Appendix D. The Normalization Algorithm
Bibliography
Index of Symbols
Index of Subjects

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