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Proof-theoretical analysis of order relations

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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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Authors and Affiliations

  1. Department of Philosophy, P.O. Box 9, Siltavuorenpenger 20A, 00014, Finland

    Sara Negri & Jan von Plato

  2. Department of Computer Science, Chalmess University of Technology, 41296, Göteborg, Sweden

    Thierry Coquand

Authors
  1. Sara Negri
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  2. Jan von Plato
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  3. Thierry Coquand
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Correspondence to Sara Negri.

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Mathematics Subject Classification (2000): 03F05, 06A05, 06A06

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Negri, S., Plato, J. & Coquand, T. Proof-theoretical analysis of order relations. Arch. Math. Logic 43, 297–309 (2004). https://doi.org/10.1007/s00153-003-0209-8

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  • DOI: https://doi.org/10.1007/s00153-003-0209-8

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