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Proof-theoretical analysis of order relations

Journal article
Authors S. Negri
J. von Plato
Thierry Coquand
Published in Archive for mathematical logic
Volume 43
Issue 3
Pages 297-309
ISSN 0933-5846
Publication year 2004
Published at Department of Computer Science and Engineering, Computing Science, Programming Logic
Pages 297-309
Language en
Links dx.doi.org/10.1007/s00153-003-0209-...
Subject categories Computer and Information Science

Abstract

A proof-theoretical analysis of elementary theories of order relations is effected through the formulation of order axioms as mathematical rules added to contraction-free sequent calculus. Among the results obtained are proof-theoretical formulations of conservativity theorems corresponding to Szpilrajn’s theorem on the extension of a partial order into a linear one. Decidability of the theories of partial and linear order for quantifier-free sequents is shown by giving terminating methods of proof-search.

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