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...
Abstract We extend Barbanera and Berardi's symmetric lambda calculus [2] to second order classical propositional logic and prove its strong normalization.
We introduce λµ→∧∨⊥ , an extension of Parigot’s λµ-calculus where disjunction is taken as a primitive. The associated reduction relation, which includes the permutati...
We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the meaning of the new notion and its a...
A new complete characterization of β-strong normalization is given, both in the classical and in the lazy λ-calculus, through the notion of potential valuability inside two suit...