Recently, different forgetting approaches for knowledge bases expressed in different logics were proposed. For EL terminologies containing each atomic concept at most once on the left-hand side, an approach has been proposed based on sufficient, but not necessary acyclicity conditions. In this paper, we propose an approach for computing a uniform interpolant for general EL terminologies. We fir...

Let a sufficiently smooth function f on [−1, 1] be sampled at n + 1 equispaced points, and let k ≥ 0 be given. An Euler–Maclaurin interpolant to the data is defined, consisting of a sum of a degree k algebraic polynomial and a degree n trigonometric polynomial, which deviates from f by O(n−k) and whose integral is equal to the order k Euler–Maclaurin approximation of the integral of f . This in...

The linear arithmetic solver in Yices was specifically designed for SMT provers, providing fast support for operations like adding and deleting constraints. We give a procedure for developing interpolants based on the results of the Yices arithmetic solver. For inequalities over real numbers, the interpolant is computed directly from the one contradictory equation and associated bounds. For int...

The evolution of SAT technology over the last decade has motivated its application in model checking, initially through the utilization of SAT in bounded model checking (BMC) and, more recently, in unbounded model checking (UMC). This paper addresses the utilization of interpolants in UMC and proposes two techniques for improving the original interpolant-based UMC algorithm. These techniques in...

In the first part of the paper we discuss minimal smoothness assumptions for the components of the solution decomposition which allow to prove robust convergence results in the energy norm for linear or bilinear finite elements on Shishkin meshes applied to convectiondiffusion problems with exponential boundary layers. In the corresponding derivation the standard Lagrange interpolant is used, i...

This paper addresses the problem of interpolating three points with a surface whose normal and orientation is also defined at those points. Conditions are derived for the existence of a quadric surface interpolant and it is shown that a cubic interpolant always exists. Finally, the paper describes a new cubic construction that provides a family of suitable surfaces with four geometrically intui...

This is a study of Favard interpolation—in which the nth derivatives of the interpolant are bounded above by a constant times the nth divided differences of the data—in the case the data is given on some subset of a rectangular lattice in R k. In some instances, depending on the geometry of this subset, we construct a Favard interpolant, and in other instances, we prove that none exists.

Cumulative chord C piecewise-cubics, for unparameterized data from regular curves in R , are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C piecewise-cubic interpolant. Theoretical estimates of orders of approximation are establis...

A Craig interpolant for a mutually inconsistent pair of formulas (A,B) is a formula that is (1) implied by A, (2) inconsistent with B, and (3) expressed over the common variables of A and B. An interpolant can be efficiently derived from a refutation of A ∧ B, for certain theories and proof systems. We will discuss a number of applications of this concept in finiteand infinite-state model check...