“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 48
School of Mathematics
  Title:   Basic propositional calculus II: Interpolation
1.  W. Ruitenburg
2.  M. Ardeshir
  Status:   Published
  Journal: Arch. Math. Logic
  No.:  5
  Vol.:  40
  Year:  2001
  Pages:   349-364
  Supported by:  IPM
Let L and N be propositional languages over Basic Propositional Calculus, and M=LN. We prove two different but interrelated interpolation theorems. First, suppose that II is a sequent theory over L, and Σ∪{ CC′} is a set of sequents over N, such that II, Σ\vdash CC′. Then there is a sequent theory Φ over M such that Π\vdash Φ and Φ,Σ\vdash CC′. Second, let A be a formula over L, and C1,C2 be formulas over N, such that AC1\vdash C2. Then there exists a formula B over M such that A\vdash B and BC1\vdash C2.

Download TeX format
back to top
scroll left or right