On P-Interpolation in Local Theory Extensions and Applications to the Study of Interpolation in the Description Logics L, L⁺

We study the P-interpolation property for certain local theory extensions, and use these results for proving <=-interpolation in classes of semilattices with monotone operators. For computing the <=-interpolating terms, we use a hierarchic approach. We use these results for the study of (sic)-interpolation in the description logics epsilon L and epsilon L+.