Deep Inference and Symmetry in Classical Proofs

By (author) Kai Brunnler

Extent: 101, 101 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Language: English

(Paperback) (Published)

(January 2004)

ISBN: 9783832504489

5.71 x 8.27 inches

Price: $61.00

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Synopsis
Contributing Authors

In this thesis we see deductive systems for classical propositionaland predicate logic which use deep inference, i.e. inference rules apply arbitrarily deep inside formulas, and a certain symmetry, which provides an involution on derivations. Like sequent systems, they have a cut rule which is admissible. Unlike sequent systems, they enjoy various new interesting properties. Notonly the identity axiom, but also cut, weakening and even contraction are reducible to atomic form. This leads to inference rules that are local, meaning that the effort of applying them is bounded, and finitely generating, meaning that, given a conclusion, there is only a finite number of premises to choose from. The systems also enjoy new normal forms for derivations and, in the propositional case, a cut elimination procedure that is drastically simpler than the ones for sequent systems.

By (author) Kai Brunnler

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Deep Inference and Symmetry in Classical Proofs

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