Affiliations: LSIS (UMR-CNRS 6186), Université du Sud Toulon-Var, Bât. R, BP.20132, 83957 La Garde Cedex, France E-mail: {chan.leduc}@univ-tln.fr | Laboratoire I3S, UNSA-CNRS, 2000 route des lucioles, Les Algorithmes - bât. Euclide B, BP.121, 06903 Sophia Antipolis Cedex, France E-mail: {nhan.le-thanh}@unice.fr | LSR-IMAG, BP 72, 38402 St Martin d'Heres Cedex, France E-mail: {marie-christine.rousset}@imag.fr
Note: [] Corresponding author. Chan Le Duc, LSIS (UMR-CNRS 6186), Université du Sud Toulon-Var, Bât. R, BP.20132, 83957 La Garde Cedex, France.
Abstract: This paper introduces a compact representation which helps to avoid the exponential blow-up in space of the Least Common Subsumer (lcs) of two ALE-concept descriptions. Based on the compact representation we define a space of specific graphs which represents all ALE-concept descriptions including the lcs. Next, we propose an algorithm exponential in time and polynomial in space for deciding subsumption between concept descriptions represented by graphs in this space. These results provide better understanding of the double exponential blow-up of the approximation of ALC-concept descriptions by ALE-concept descriptions: double exponential size of the approximation in the ordinary representation is unavoidable in the worst case.
Keywords: Description logics, Least Common Subsumer, approximation
