A Compact Representation for Least Common Subsumers in the description logic ALE

This paper introduces a compact representation which helps to avoid the exponential blow-up 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 inavoidable in the worst