On the Power of Substitution in the Calculus of Structures

Lutz Strassburger (1, 2) , Novak Novakovic (2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 PARSIFAL - Proof search and reasoning with logic specifications

In this paper we give a direct and simple proof of the known fact that Frege systems with substitution can be p-simulated by the calculus of structures extended with the substitution rule. This is done without referring to extended Frege systems. In the second part of the paper, we then show that the cut-free calculus of structures with substitution is p-equivalent to the cut-free calculus of structures with extension.

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]; Complexité [cs.CC]

Lutz Strassburger, Novak Novakovic. On the Power of Substitution in the Calculus of Structures. ACM Transactions on Computational Logic, 2015, 16 (3), ⟨10.1145/2701424⟩. ⟨hal-00925707⟩