Strong Normalisation of Cut-Elimination in Classical Logic

In this paper we present a strongly normalising cut-elimination procedure for classical logic. This procedure adapts Gentzen’s standard cut-reductions, but is less restrictive than previous strongly normalising cut-elimination procedures. In comparison, for example, with works by Dragalin and Danos et al., our procedure requires no special annotations on formulae and allows cut-rules to pass over other cut-rules. In order to adapt the notion of symmetric reducibility candidates for proving the strong normalisation property, we introduce a novel term assignment for sequent proofs of classical logic and formalise cut-reductions as term rewriting rules.

• Type: Conference
• Year: 1999
• Where: TLCA
• Authors: Christian Urban, Gavin M. Bierman
• Keywords: Classical Logic, Normalising Cut-elimination Procedures, Procedure Adapts Gentzen, Theoretical Computer Science, TLCA 1999