On the form of witness terms

Stefan Hetzl (1)

1 PPS - Preuves, Programmes et Systèmes

We investigate the development of terms during cut-elimination in first-order logic and Peano arithmetic for proofs of existential formulas. The form of witness terms in cut-free proofs is characterized in terms of structured combinations of basic substitutions. Based on this result, a regular tree grammar computing witness terms is given and a class of proofs is shown to have only elementary cut-elimination.

Domaines: Logique [math.LO]

Stefan Hetzl. On the form of witness terms. Archive for Mathematical Logic, 2010, 49 (5), pp.529-554. ⟨10.1007/s00153-010-0186-7⟩. ⟨hal-00498696⟩