Tags:Description Logic, iALC, Intuitionistic Logic and Natural Deduction
Abstract:
In this paper we present a new labelled Natural Deduction calculus for the logic iALC, an intuitionistic description logic with nominals originally designed to reason over laws and other normative sentences in general. Even though this logic already has a formalised Sequent Calculus system, in practice Natural Deduction is more adequate in regards to making proofs more explainable - which is further aided by our use of labels. Finally, we prove soundness and normalisation for the new Natural Deduction system, and show its completeness.
A Labelled Natural Deduction System for an Intuitionistic Description Logic with Nominals