5 papers
Admissibility of the Structural Rules in the Sequent Calculus with Equality
Franco Parlamento, Flavio Previale
On the ground of a general theorem concerning the admissibility of the structural rules in sequent calculi with additional atomic rules, we develop a proof theoretic analysis for s…
Absorbing the Structural Rules in the Sequent Calculus with Additional Atomic Rules
Franco Parlamento, Flavio Previale
We show that if the structural rules are admissible over a set R of atomic rules, then they are admissible in the sequent calculus obtained by adding the rules in R to G3[mic]. Two…
A simplified version of the Sequent Calculus G3[mic]^=
Franco Parlamento, Flavio Previale
We show that the Replacement Rule in the sequent calculus G3[mic]}^=, for first order languages with function symbols and equality, can be replaced by the simpler rule in which the…
The Cut Elimination and the Nonlengthening Property for the Sequent Calculus with Equality
Franco Parlamento, Flavio Previale
We show how Leibnitz.s indiscernibility principle and Gentzen's original work lead to extensions of the sequent calculus to first order logic with equality and investigate the cut…
Contraction Elimination in Sequent Based Ground Equational Calculus
F. Parlamento, F. Previale
In "Cut Elimination for Gentzen's Sequent Calculus with Equality and Logic of Partial Terms" LNCS 7750,161-172(2013), we have shown that the cut rule is eliminable in two ground eq…