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Lectures on Linear Logic [Mīkstie vāki]

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Lectures on Linear LogicPalielināt
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Lecture notes originating in a course given at the U. of Amsterdam, Spring 1991, explore in depth linear logic and its implications, for readers with some sophistication in logic. Annotation copyright Book News, Inc. Portland, Or.

The initial sections of this text deal with syntactical matters such as logical formalism, cut-elimination, and the embedding of intuitionistic logic in classical linear logic. Concluding chapters focus on proofnets for the multiplicative fragment and the algorithmic interpretation of cut-elimination in proofnets.
1. Introduction;
2. Sequent calculus for linear logic;
3. Some
elementary syntactic results;
4. The calculus of two implications: a
digression;
5. Embeddings and approximations;
6. Natural deduction systems
for linear logic;
7. Hilbert-type systems;
8. Algebraic semantics;
9.
Combinatorial linear logic;
10. Girard domains;
11. Coherence in symmetric
monoidal categories;
12. The storage operator as a coffee comonoid;
13.
Evaluation in typed calculi;
14. Computation by lazy evaluation in CCC's;
15.
Computation by lazy evaluation in SMC's and ILC's;
16. The categorical and
linear machine;
17. Proofnets for the multiplicative fragment;
18. The
algorithm of cut elimination for proof nets;
19. Multiplicative operators;
20. The undecidability of linear logic;
21. Cut elimination and strong
normalization; References; Index.