In predicate logic, the proof that a theorem P holds in a theory Th is typically conducted in natural deduction or in the sequent calculus using all the information contained in t...
act Completion (Full Version) Guillaume Burel Claude Kirchner August 6, 2007 Deduction Modulo implements Poincar´e’s principle by identifying deduction and computation as diff...
We define a generic notion of cut that applies to many first-order theories. We prove a generic cut elimination theorem showing that the cut elimination property holds for all theo...
In 1973, Parikh proved a speed-up theorem conjectured by G¨odel 37 years before: there exist arithmetical formulæ that are provable in first order arithmetic, but whose shorter ...