We implement and evaluate a recently introduced method to compute uniform interpolants for ontologies specified in the description logic ALC. The aim of uniform interpolation is to reformulate an ontology such that it only uses a specified set of symbols, while preserving consequences that involve these symbols. Uniform interpolation is useful to applications in ontology engineering and modular...

A common problem in software model checking is the automatic computation of accurate loop invariants. Loop invariants can be derived from interpolants for every path leading through the corresponding loop header. However, in practice, the consideration of single paths often leads to very path specific interpolants. Inductive invariants can only be derived after several iterations by also taking...

We present a method to compute uniform interpolants with fixpoints for ontologies specified in the description logic ALC. The aim of uniform interpolation is to reformulate an ontology such that it only uses a specified set of symbols, while preserving consequences that involve these symbols. It is known that in ALC uniform interpolants cannot always be finitely represented. Our method computes...

EL is a popular description logic, used as a core formalism in large existing knowledge bases. Uniform interpolants of knowledge bases are of high interest, e.g. in scenarios where a knowledge base is supposed to be partially reused. However, to the best of our knowledge no procedure has yet been proposed that computes uniform EL interpolants of general EL terminologies. Up to now, also the bou...

In this paper, localization properties of trigonometric polynomial Hermite operators are discussed. In particular, time frequency uncertainty and operator norms are compared for the diierent types of fundamental interpolants which serve as scaling functions for a trigono-metric multiresolution analysis. x1. Introduction Recently, several diierent approaches to periodic multiresolution analyses ...

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifierfree interpolants in general. In this paper, we show that it is possible to obtain quantifier-free interpolants for a Skolemized vers...

We develop a clausal resolution-based approach for computing uniform interpolants of TBoxes formulated in the description logicALC when such uniform interpolants exist. We also present an experimental evaluation of our approach and its applications to concept forgetting, ontology obfuscation and logical difference on real-life ALC ontologies. Our results indicate that in many practical cases a ...

Voronoi based interpolation employs the concept of natural neighbors to define an interpolating function over discrete data known at scattered sample points. In this work we review the two main concepts for improving interpolation continuity inside the convex hull of the sample domain and compare four natural neighbor interpolants of C and C continuity. We give a visual presentation of all inte...