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arXiv · 1705.04606

Integrating a Global Induction Mechanism into a Sequent Calculus

David M. Cerna·Michael Peter Lettmann
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Abstract

Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof theoretic properties of the calculus. To the best of our knowledge, there are no such calculi which allow cut-elimination to a normal form with the subformula property, i.e. every formula occurring in the proof is a subformula of the end sequent. Proof schemata are a variant of LK-proofs able to simulate induction by linking proofs together. There exists a schematic normal form which has comparable proof theoretic behaviour to normal forms with the subformula property. However, a calculus for the construction of proof schemata does not exist. In this paper, we introduce a calculus for proof schemata and prove soundness and completeness with respect to a fragment of the inductive arguments formalizable in Peano arithmetic.

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David M. Cerna, Michael Peter Lettmann. 2017-05-12. Integrating a Global Induction Mechanism into a Sequent Calculus. https://doi.org/10.1007/978-3-319-66902-1_17

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