Modular Cut-Elimination: Finding Proofs or Counterexamples
- Cite this paper as:
- Ciabattoni A., Terui K. (2006) Modular Cut-Elimination: Finding Proofs or Counterexamples. In: Hermann M., Voronkov A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2006. Lecture Notes in Computer Science, vol 4246. Springer, Berlin, Heidelberg
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.
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