Computing Theory Prime Implicates in Modal Logic

The algorithm to compute theory prime implicates, a generalization of prime implicates, in propositional logic has been suggested in [16]. In this paper we have extended that algorithm to compute theory prime implicates of a knowledge base X with respect to another knowledge base Y using [2], where Y is a propositional knowledge base and X |= Y , in modal system T and we have also proved its correctness. We have also proved that it is an equivalence preserving knowledge compilation and the size of theory prime implicates of X with respect to Y is less than the size of the prime implicates of X ∪ Y . We have also extended the query answering algorithm in modal logic.