Download PDFOpen PDF in browserFrom Classical Extensional Higher-Order Tableau to Intuitionistic Intentional Natural Deduction16 pages•Published: May 26, 2013AbstractWe define a translation that maps higher-order formulas provable in a classical extensional setting to semantically equivalent formulas provable in an intuitionistic intensional setting. For the classical extensional higher-order proof system we define a Henkin-complete tableau calculus. For the intuitionistic intensional higher-order proof system we give a natural deduction calculus. We prove that tableau provability of a formula implies provability of a translated formula in the natural deduction calculus. Implicit in this proof is a method for translating classical extensional tableau refutations into intuitionistic intensional natural deduction proofs.Keyphrases: analytic tableaux, classical, extensional, higher order logic, intensional, intuitionistic, proof theory, simple type theory, tableaux In: Jasmin Christian Blanchette and Josef Urban (editors). PxTP 2013. Third International Workshop on Proof Exchange for Theorem Proving, vol 14, pages 27-42.
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