Sequent Calculi for $${\mathsf {SCI}}$$ SCI

Studia Logica 106 (3):541-563 (2018)
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Abstract

In this paper we are applying certain strategy described by Negri and Von Plato :418–435, 1998), allowing construction of sequent calculi for axiomatic theories, to Suszko’s Sentential calculus with identity. We describe two calculi obtained in this way, prove that the cut rule, as well as the other structural rules, are admissible in one of them, and we also present an example which suggests that the cut rule is not admissible in the other.

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10.1007/s11225-017-9754-8

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References found in this work

Cut Elimination in the Presence of Axioms.Sara Negri & Jan Von Plato - 1998 - Bulletin of Symbolic Logic 4 (4):418-435.
Investigations into the sentential calculus with identity.Roman Suszko & Stephen L. Bloom - 1972 - Notre Dame Journal of Formal Logic 13 (3):289-308.
For Oiva Ketonen's 85th birthday.Sara Negri & Jan von Plato - 1998 - Bulletin of Symbolic Logic 4 (4):418-435.
Proof-theoretical analysis of order relations.Sara Negri, Jan von Plato & Thierry Coquand - 2004 - Archive for Mathematical Logic 43 (3):297-309.
A uniform proof procedure for SCI tautologies.Aileen Michaels - 1974 - Studia Logica 33 (3):299 - 310.

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