# interpolation property

A logic is said to have the interpolation property if whenever $\phi(R,S)\rightarrow\psi(R,T)$ holds, then there is a sentence $\theta(R)$, so that both $\phi(R,S)\rightarrow\theta(R)$ and $\theta(R)\rightarrow\psi(R,T)$ hold, where $R,S$ and $T$ are some sets of symbols that occur in the formulas, $R$ being the set of symbols common to both $\phi$ and $\psi$.

The interpolation property holds for first order logic. The interpolation property is related to Beth definability property and Robinson’s consistency property. Also, a natural generalisation is the concept $\Delta$-closed logic.

Title interpolation property InterpolationProperty 2013-03-22 13:49:36 2013-03-22 13:49:36 CWoo (3771) CWoo (3771) 7 CWoo (3771) Definition msc 03B99 interpolation property