On P-Interpolation in Local Theory Extensions and Applications to the Study of Interpolation in the Description Logics EL, EL^+
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We study the problem of P-interpolation, where P is a set of binary predicate symbols, for certain classes of local extensions of a base theory. For computing the P-interpolating terms, we use a hierarchic approach: This allows us to compute the interpolating terms using a method for computing interpolating terms in the base theory. We use these results for proving ≤-interpolation in classes of semilattices with monotone operators; we show, by giving a counterexample, that ≤-interpolation does not hold if by "shared" symbols we mean just the common symbols. We use these results for the study of ⊑-interpolation in the description logics EL and EL^+.
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