A Tableaux-Based Decision Procedure for Multi-parameter Propositional Schemata

Cerna, David M.

doi:10.1007/978-3-319-08434-3_6

Cited by 1 publication

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“…They developed a tableau based decision procedure for the satisfiability of a monadic 3 fragment of this logic. An extension to a special case of multiple parameters was also investigated by D. Cerna [13]. In a more recent work, V. Aravantinos et al [6] introduced a superposition resolution calculus for a clausal representation of indexed propositional logic.…”

Section: Introductionmentioning

confidence: 99%

Integrating a Global Induction Mechanism into a Sequent Calculus

Cerna

Lettmann

2017

Lecture Notes in Computer Science

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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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Section: Introductionmentioning

confidence: 99%