On the Verification of Parametric Systems

We present an approach to the verification of systems for whose description some elements - constants or functions - are underspecified and can be regarded as parameters, and, in particular, describe a method for automatically generating constraints on such parameters under which certain safety conditions are guaranteed to hold. We present an implementation and illustrate its use on several examples.Comment: 26 pages. arXiv admin note: text overlap with arXiv:1910.0520

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

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 ${\cal EL}^+$.Comment: 33 page