Modular Cut-Elimination: Finding Proofs or Counterexamples [chapter]

Agata Ciabattoni, Kazushige Terui
2006 Lecture Notes in Computer Science  
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) multipleconclusion sequent calculi with generalized quantifiers. We provide a "universal" modular cut-elimination procedure that works uniformly for any standard calculus satisfying our conditions. The
more » ... failure of these conditions generates counterexamples for modular cut-elimination and, in certain cases, for cut-elimination.
doi:10.1007/11916277_10 fatcat:zgzezwfyy5fehnhtp2eicts6iy