Abstract
The aim of the paper is to present two natural deduction systems for Intuitionistic Sentential Calculus with Identity (ISCI); a syntactically motivated \(\mathsf {ND}^1_{\mathsf {ISCI}}\) and a semantically motivated \(\mathsf {ND}^2_{\mathsf {ISCI}}\). The formulation of \(\mathsf {ND}^1_{\mathsf {ISCI}}\) is based on the axiomatic formulation of ISCI. Its rules cannot be straightforwardly classified as introduction or elimination rules; ISCI-specific rules are based on axioms characterizing the identity connective. The system does not enjoy the standard subformula property, but due to the normalization procedure non-subformulas can label only leaves of proofs. In \(\mathsf {ND}^2_{\mathsf {ISCI}}\), we propose only two general identity-related rules, in reference to the treatment of the identity connective in First-Order Logic.
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Chlebowski, S., Gawek, M. & Tomczyk, A. Natural Deduction Systems for Intuitionistic Logic with Identity. Stud Logica 110, 1381–1415 (2022). https://doi.org/10.1007/s11225-022-09995-0
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DOI: https://doi.org/10.1007/s11225-022-09995-0