Skip to Main content Skip to Navigation
New interface
Conference papers

Semantic A-translation and Super-consistency entail Classical Cut Elimination

Abstract : We show that if a theory R defined by a rewrite system is super-consistent, the classical sequent calculus modulo R enjoys the cut elimination property, which was an open question. For such theories it was already known that proofs strongly normalize in natural deduction modulo R, and that cut elimination holds in the intuitionistic sequent calculus modulo R. We first define a syntactic and a semantic version of Friedman's A-translation, showing that it preserves the structure of pseudo-Heyting algebra, our semantic framework. Then we relate the interpretation of a theory in the A-translated algebra and its A-translation in the original algebra. This allows to show the stability of the super-consistency criterion and the cut elimination theorem.
Complete list of metadata

Cited literature [18 references]  Display  Hide  Download
Contributor : Olivier Hermant Connect in order to contact the contributor
Submitted on : Sunday, January 5, 2014 - 10:17:33 PM
Last modification on : Tuesday, October 25, 2022 - 4:20:36 PM
Long-term archiving on: : Thursday, April 10, 2014 - 4:11:20 PM


Files produced by the author(s)



Lisa Allali, Olivier Hermant. Semantic A-translation and Super-consistency entail Classical Cut Elimination. LPAR 19 - 19th Conference on Logic for Programming, Artificial Intelligence, and Reasoning - 2013, Bernd Fischer, Geoff Sutcliffe, Dec 2013, Stellenbosch, South Africa. pp.407-422, ⟨10.1007/978-3-642-45221-5_28⟩. ⟨hal-00923915⟩



Record views


Files downloads