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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Deep Inference and Symmetry in Classical Proofs

Deep Inference and Symmetry in Classical Proofs

Brunnler, Kai

Paperback

General ComputersGeneral Mathematics

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ISBN10: 3832504486
ISBN13: 9783832504489
Publisher: Logos Verlag Berlin
Published: Jan 15 2004
Pages: 101
Weight: 0.30
Height: 0.33 Width: 5.60 Depth: 7.88
Language: English
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.

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