Archive for Mathematical Logic 40 (5):349-364 (2001)

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∪ {C⇒C′} is a set of sequents over ?, such that Π,Σ⊢C⇒C′. Then there is a sequent theory Φ over ℳ such that Π⊢Φ and Φ, Σ⊢C⇒C′. Second, let A be a formula over ℒ, and C 1, C 2 be formulas over ?, such that A∧C 1⊢C 2. Then there exists a formula B over ℳ such that A⊢B and B∧C 1⊢C 2
Keywords Key words or phrases: Basic logic – Kripke model – Interpolation
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DOI 10.1007/PL00003844
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