Rational elimination algorithm and applications

Gauss elimination algorithm for interval matrix

Euclid's Algorithm, Guass' Elimination and Buchberger's Algorithm

It is known that Euclid’s algorithm, Guass’ elimination and Buchberger’s algorithm play important roles in algorithmic number theory, symbolic computation and cryptography, and even in science and engineering. The aim of this paper is to reveal again the relations of these three algorithms, and, simplify Buchberger’s algorithm without using multivariate division algorithm. We obtain an algorith...

Rational Elimination of DL-Lite TBox Axioms

An essential task in managing description logic (DL) ontologies is the elimination of problematic axioms. Such elimination is formalised as the operation of contraction in belief change. In this paper, we investigate contraction over DL-LiteR TBoxes. In belief change, a well known approach for defining contraction is via epistemic entrenchments which are preference orderings over formulas. The ...

Rational Orthonormal Functions and Applications

Acknowledgement I am very grateful to Professor Ferenc Schipp for initiating me on the field of the approximation theory, for his advices and remarks without them this thesis would have been impossible. I am also indebted to the members of the Department of Numerical Analysis of the Eötvös Loránd University for their support during the years. I am especially grateful to Professor József Bokor i...

Density Elimination and Rational Completeness for First-Order Logics

Density elimination by substitutions is introduced as a uniformmethod for removing applications of the Takeuti-Titani density rule from proofs in firstorder hypersequent calculi. For a large class of calculi, density elimination by this method is guaranteed by known sufficient conditions for cut-elimination. Moreover, adding the density rule to any axiomatic extension of a simple first-order lo...