Tractable Concept Languages

Francesco M. Donini, Maurizio Lenzerini, Daniele Nardi, Werner Nutt

Abstract:

We present two concept languages, called PL1 and PL2 which are extensions of TC. We prove that the subsumption problem in these languages can be solved in polynomial time. Both languages include a construct for expressing inverse roles, which has not been considered up to now in tractable languages. In addition, PL1 includes number restrictions and negation of primitive concepts, while Pl2 includes role conjunction and role chaining.

By exploiting recent complexity results, we show that none of the constructs usually considered in concept languages can be added to PL1 and PL2 without losing tractabtlity. Therefore, on the assumption that Languages are characterized by the set of constructs they provide, the two languages presented in this paper provide a solution to the problem of singling out an optimal trade-off between expressive power and computational complexity.