Proof-theoretic versus Model-theoretic Consequence

Abstract

Model-theoretic and proof-theoretic notions of logical consequence are compared. According to standard semantics, they rely on the idea of the transmission of a categorical concept (truth, canonical provability) from the premisses to the conclusion of a hypothetical consequence statement. It is argued that the hypothetical should be given conceptual priority over the categorical, which for formal systems means a conceptual preference of the sequent calculus over the calculus of natural deduction.