Section: New Results

Admissible Tools in the Kitchen of Intuitionistic Logic

Participants : Matteo Manighetti, Andrea Condoluci.

In this work we study the computational meaning of the inference rules that are admissible, but not derivable, in intuitionistic logic [16].

An inference rule is admissible for a logic if whenever its antecedent is derivable, its conclusion was already derivable without the rule. In classical logic, whenever this is the case, then also the implication between antecedent and conclusion is derivable. The notion of an admissible rule is therefore internalized in the logic.

This is not the case for intuitionistic logic, and some rules that are admissible are not derivable: therefore they need reasoning outside the usual intuitionistic logic in order to be reduced to purely intuitionistic derivation.

In this work we propose a proof system with term annotations and reduction rules to give a computational meaning to these reductions.