Proof-Theoretical Coherence

Description

This book in categorial proof theory formulates in terms of category theory a generalization close to linear algebra of the notions of distributive lattice and Boolean algebra. These notions of distributive lattice category and Boolean category codify a plausible nontrivial notion of identity of proofs in classical propositional logic, which is in accordance with Gentzen’s cut-elimination procedure for multiple-conclusion sequents modified by admitting new principles called union of proofs and zero proofs. It is proved that these notions of category are coherent in the sense that there is a faithful structure-preserving functor from freely generated distributive lattice categories and Boolean categories into the category whose arrows are relations between finite ordinals-a category related to generality of proofs and to the notion of natural transformation. These coherence results yield a simple decision procedure for equality of proofs. Coherence in the same sense is also proved for various more general notions of category that enter into the notions of distributive lattice category and Boolean category. Some of these coherence results, like those for monoidal and symmetric monoidal categories are well known, but are here presented in a new light. The key to this categorification of the proof theory of classical propositional logic is distribution of conjunction over disjunction that is not an isomorphism as in cartesian closed categories.

Disclaimer:
Contents of this page are indexed from the Internet. All actions are under your responsability. Email us to report illegal contents or external links and we'll remove them immediately.

Please check the description for download links if any or do a search to find alternative books.

Can't Download?
Please search mirrors if you can't find download links for "Proof-Theoretical Coherence" in "Description" and someone else may update the links. Check the comments when back to find any updates.

Search Mirrors
Maybe some mirror pages will be helpful, search this book at top of this page or click here to find more info.

1. Ebooks list page : 3082
2. Natural Deduction: A Proof-Theoretical Study
3. Basic Proof Theory (Cambridge Tracts in Theoretical Computer Science)
4. Reductive Logic and Proof-search: Proof Theory, Semantics, and Control
5. The Proof Is in the Pudding: The Changing Nature of Mathematical Proof (ReUp)
6. Applied Proof Theory: Proof Interpretations and their Use in Mathematics (repost)
7. Applied Proof Theory: Proof Interpretations and their Use in Mathematics (Springer Monographs in Mathematics)
8. Proof Theory and Logical Complexity : Volume I (Studies in Proof Theory)
9. Coherence in Categories
10. Athanasius: The Coherence of His Thought
11. Nanophysics: Coherence and Transport
12. Handbook of Optical Coherence Tomography
13. Handbook of Optical Coherence Tomography
14. The Coherence of Kant's Transcendental Idealism
15. The Coherence of Kant's Transcendental Idealism
16. Optical Coherence and Quantum Optics