Proof-theoretical analysis of order relations

Archive for Mathematical Logic 43 (3):297-309 (2004)
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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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Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
Proof analysis in intermediate logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1):71-92.
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