Given a theory T and two formulas A and B jointly unsatisfiable in T , a theory interpolant of A and B is a formula I such that (i) its non-theory symbols are shared by A and B, (ii) it is entailed by A in T , and (iii) it is unsatisfiable with B in T . Theory interpolants are used in model checking to accelerate the computation of reachability relations. We present a novel method for computing...

One of the main challenges in software verification is efficient and precise analysis of programs with procedures and loops. Interpolation methods remain among the most promising techniques for such verification. To accommodate the demands of various programming language features, over the past years several extended forms of interpolation have been introduced. We give a precise ontology of suc...

We propose a method for forgetting concept symbols and non-transitive roles symbols of SHQ-ontologies, or for computing uniform interpolants in SHQ. Uniform interpolants restrict the symbols occuring in an ontology to a specified set, while preserving all logical entailments that can be expressed using this set in the description logic under consideration. Uniform interpolation has applications...

Abstract We propose a novel formulation of elastic materials based on high‐order interpolants, which fits accurately complex behaviors, but remains conservative. The proposed interpolants can be regarded as high‐dimensional extension radial basis functions, and they allow the interpolation derivatives energy, in particular stress stiffness. Given parameterization elasticity models, we devise an...

Interpolation is an important technique in computer aided verification and static analysis of programs. In particular, interpolants extracted from so-called local proofs are used in invariant generation and bounded model checking. An interpolant extracted from such a proof is a boolean combination of formulas occurring in the proof. In this talk we first describe a technique of generating and o...

We introduce a general definition of refinable Hermite interpolants and investigate their general properties. We also study a notion of symmetry of these refinable interpolants. Results and ideas from the extensive theory of general refinement equations are applied to obtain results on refinable Hermite interpolants. The theory developed here is constructive and yields an easyto-use constructio...

We discuss a generalization of Berrut’s first and second rational interpolants to the case equally spaced points on triangle in R2.

Algorithms for computing Craig interpolants have several applications in program verification. Though different algorithms exist, the relationship between them and the properties of the interpolants they generate are not well understood. This paper is a study of interpolation algorithms for propositional resolution proofs. We show that existing interpolation algorithms are abstractions of a mor...

Uniform interpolation and the dual task of forgetting restrict the ontology to a specified subset of concept and role names. This makes them useful tools for ontology analysis, ontology evolution and information hiding. Most previous research focused on uniform interpolation of TBoxes. However, especially for applications in privacy and information hiding, it is essential that uniform interpola...