On the difference of Horn theories

In this payer. we consider computing the difference between two Horn theori es. This problem may arise, for example, if we take care of a theory change in a knowledge base. In general, the difference of Horn theories is not Ho rn. Therefore, we consider Horn approximations of the difference in terms o f Horn cores (i.e., weakest Horn theories included in the difference) and t he Horn envelope (i.e., the strongest Horn theory containing the difference ), which have been proposed and analyzed extensively in the literature. We study the problem under the familiar representation of Horn theories by Hor n CNFs. as well as under the recently proposed model-based representation i n terms of the characteristic models. For all problems and representations polynomial time algorithms or proofs of intractability for the propositiona l ease are provided: thus, our work gives a complete picture of the tractab ility-intractability frontier in the propositional Horn theories. (C) 2000 Academic Press.