Logic for Programming, Artificial Intelligence, and Reasoning

Volume 4246 of the series Lecture Notes in Computer Science pp 135-149

Modular Cut-Elimination: Finding Proofs or Counterexamples

  • Agata CiabattoniAffiliated withInstitute für Diskrete Mathematik und Geometrie, TU Wien
  • , Kazushige TeruiAffiliated withNational Institute of Informatics

* Final gross prices may vary according to local VAT.

Get Access


Modular cut-elimination is a particular notion of ”cut-elimination in the presence of non-logical axioms” that is preserved under the addition of suitable rules. We introduce syntactic necessary and sufficient conditions for modular cut-elimination for standard calculi, a wide class of (possibly) multiple-conclusion sequent calculi with generalized quantifiers. We provide a ”universal” modular cut-elimination procedure that works uniformly for any standard calculus satisfying our conditions. The failure of these conditions generates counterexamples for modular cut-elimination and, in certain cases, for cut-elimination.