Automated Reasoning in Quantified Non-Classical Logics

This paper introduces a non-clausal connection calculus for intuitionistic first-order logic. It is an extension of the non-clausal connection calculus for classical logic by prefixes and an additional prefix unification, which encode the Kripke semantics of intuitionistic logic. nanoCoP-i is a first implementation of this intuitionistic non-clausal connection calculus. Details of the compact Prolog code are presented, which extends the non-clausal connection prover nanoCoP for classical logic. Experimental evaluations on the ILTP and the TPTP problem libraries show a solid performance of the nanoCoP-i prover. In comparison to the ileanCoP prover, the resulting non-clausal proofs are not only shorter, but can also be more easily translated into, e.g., sequent proofs.