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Basic propositional calculus II. Interpolation

Ardeshir, M ; Sharif University of Technology | 2001

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  1. Type of Document: Article
  2. DOI: 10.1007/PL00003844
  3. Publisher: Springer New York , 2001
  4. Abstract:
  5. Let ℒ and script N be propositional languages over Basic Propositional Calculus, and script M = ℒ ∩ script N. We prove 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 script N, such that Π, Σ ⊢ C ⇒ C′. Then there is a sequent theory Φ over script N such that Π ⊢ Φ and Φ, Σ ⊢ C ⇒ C′. Second, let A be a formula over ℒ, and C1, C2 be formulas over script N, such that A ∧ C1 ⊢ C2. Then there exists a formula B over script M such that A ⊢ B and B ∧ C1 ⊢ C2
  6. Keywords:
  7. Basic logic ; Interpolation ; Kripke model
  8. Source: Archive for Mathematical Logic ; Volume 40, Issue 5 , 2001 , Pages 349-364 ; 09335846 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/PL00003844