A formal framework for specifying sequent calculus proof systems

Intuitionistic logic and intuitionistic type systems are commonly used as frameworks for the specification of natural deduction proof systems. In this paper we show how to use classical linear logic as a logical framework to specify sequent calculus proof systems and to establish some simple consequ...

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Bibliographic Details
Published in:Theoretical computer science Vol. 474; pp. 98 - 116
Main Authors: Miller, Dale, Pimentel, Elaine
Format: Journal Article
Language:English
Published: Elsevier B.V 25.02.2013
Elsevier
Subjects:
Cut elimination
Linear logic
Logical frameworks
Proof systems
Sequent calculus
Linear logic
Cut elimination
Proof systems
Logical frameworks
Sequent calculus
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:Intuitionistic logic and intuitionistic type systems are commonly used as frameworks for the specification of natural deduction proof systems. In this paper we show how to use classical linear logic as a logical framework to specify sequent calculus proof systems and to establish some simple consequences of the specified sequent calculus proof systems. In particular, derivability of an inference rule from a set of inference rules can be decided by bounded (linear) logic programming search on the specified rules. We also present two simple and decidable conditions that guarantee that the cut rule and non-atomic initial rules can be eliminated.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2012.12.008