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Archive for Mathematical Logic

, Volume 43, Issue 3, pp 297–309 | Cite as

Proof-theoretical analysis of order relations

  • Sara NegriEmail author
  • Jan von Plato
  • Thierry Coquand
Article

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.

Keywords

Partial Order Linear Order Order Relation Elementary Theory Sequent Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of PhilosophyFinland
  2. 2.Department of Computer ScienceChalmess University of TechnologyGöteborgSweden

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