ExpExpExplosion: Uniform Interpolation in General EL Terminologies

Although EL is a popular logic used in large existing knowledge bases, to the best of our knowledge no procedure has yet been proposed that computes uniform EL interpolants of general EL terminologies. Up to now, also the bounds on the size of uniform EL interpolants remain unknown. In this paper, we propose an approach based on proof theory and the theory of formal tree languages to computing a finite uniform interpolant for a general EL terminology if it exists. Further, we show that, if such a finite uniform EL interpolant exists, then there exists one that is at most triple exponential in the size of the original TBox, and that, in the worst-case, no shorter interpolants exist, thereby establishing the triple exponential tight bounds on their size.