Computing the Number Restriction Deduced from the Existential Restriction in Description Logic with Primitive Negation, Existential Restriction and Number Restriction

In this paper we discuss the relation between the number restriction and existential restriction in description logic ALepsivN. We show that incompatible existential restrictions on the top conjunction of concept descriptions can deduce a number restriction, exactly speaking an at least restriction. Firstly we define the incompatible relation among the existential restrictions on the top conjunction of an ALepsivN concept description D, then we use a simple undirected graph G to describe the incompatible relation, whose vectors stand for the existential restrictions. After that we compute the maximal complete subgraph of G and the number of its vectors is our expected number in the deduced number restriction.