We present a method to compute uniform interpolants of ALC-ontologies with ABoxes. Uniform interpolants are restricted views of ontologies that only use a specified set of symbols, but share all entailments in that signature with the original ontology. This way, it allows to select or remove information from an ontology based on a signature, which has applications in privacy, ontology analysis ...

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model checking, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, litt...

Orthogonal zero interpolants (OZI) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. OZI’s can be constructed by the 3-term recurrence relation. These interpolants are found useful in the solution of constrained approximation problems and in the structure of Gauss-type quadrature rules. We present some theoretical...

Abstract The use of propositional logic and systems linear inequalities over reals is a common means to model software for formal verification. Craig interpolants constitute central building block in this setting over-approximating reachable states, e.g. as candidates inductive loop invariants. Interpolants system can be efficiently computed from Simplex refutation by applying the Farkas’ lemma...

This paper is concerned with the description of an algorithm for generating the B-nets of box splines and an algorithm based on subdivision of these B-nets for graphically displaying spline surfaces on a three-or four-directional mesh. The combination of these two algorithms is shown to compare favorably over the other existing algorithms for this purpose. 0 1 x1. Introduction It is well known ...

In this paper, a modified orthogonal linear spline (OL-spline) is used for the numerical solution of coupled nonlinear inverse reaction-diffusion problem to determine unknown boundary conditions. The convergence properties new combination are obtained. A quasi-linearization technique utilized linearize term in equations. This process produces system equations which can be solved easily. Using i...

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative that geometrically constructed and form convex of unity. With the help control polynomial theory introduced herein, Marsden identity ...

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative that geometrically constructed and form convex of unity. With the help control polynomial theory introduced herein, Marsden identity ...

We study a new simple quadrature rule based on integrating a C1 quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions and we compare this formula with Simpson’s rule.