Abstract
We present two constructive proofs of the decidability of intuitionistic propositional logic by simultaneously constructing either a counter-model or a derivation. From these proofs, we extract two programs which have a sequent as input and return a derivation or a counter-model. The search tree of these algorithms is linearly bounded by the number of connectives of the input. Soundness of these programs follows from giving a correct construction of the derivations, similarly to Hudelmaier’s work [7]; completeness from giving a correct construction of the counter-models, inspired by Miglioli, Moscato, and Ornaghi [8].
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Weich, K. (1998). Decision Procedures for Intuitionistic Propositional Logic by Program Extraction. In: de Swart, H. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1998. Lecture Notes in Computer Science(), vol 1397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69778-0_29
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DOI: https://doi.org/10.1007/3-540-69778-0_29
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