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arXiv · 2307.08843

On $P$-Interpolation in Local Theory Extensions and Applications to the Study of Interpolation in the Description Logics ${\cal EL}, {\cal EL}^+$

Dennis Peuter·Viorica Sofronie-Stokkermans·Sebastian Thunert
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Abstract

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 $\leq$-interpolation in classes of semilattices with monotone operators; we show, by giving a counterexample, that $\leq$-interpolation does not hold if by "shared" symbols we mean just the common symbols. We use these results for the study of $\sqsubseteq$-interpolation in the description logics ${\cal EL}$ and ${\cal EL}^+$.

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Dennis Peuter, Viorica Sofronie-Stokkermans, Sebastian Thunert. 2023-07-17. On $P$-Interpolation in Local Theory Extensions and Applications to the Study of Interpolation in the Description Logics ${\cal EL}, {\cal EL}^+$. https://arxiv.org/abs/2307.08843

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