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Basic Propositional Calculus II. Interpolation

II. Interpolation

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Abstract.

Let ℒ and ? be propositional languages over Basic Propositional Calculus, and ℳ = ℒ∩?. Weprove two different but interrelated interpolation theorems. First, suppose that Π is a sequent theory over ℒ, and Σ∪ {CC′} is a set of sequents over ?, such that Π,Σ⊢CC′. Then there is a sequent theory Φ over ℳ such that Π⊢Φ and Φ, Σ⊢CC′. Second, let A be a formula over ℒ, and C 1, C 2 be formulas over ?, such that AC 1C 2. Then there exists a formula B over ℳ such that AB and BC 1C 2.

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Received: 7 January 1998 / Published online: 18 May 2001

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Ardeshir, M., Ruitenburg, W. Basic Propositional Calculus II. Interpolation. Arch. Math. Logic 40, 349–364 (2001). https://doi.org/10.1007/PL00003844

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  • DOI: https://doi.org/10.1007/PL00003844

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