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 \cite{Marquis}. In this paper we have extended that algorithm to compute theory prime implicates of a knowledge base $X$ with respect to another knowledge base $\Box Y$ using \cite{Bienvenu}, where $Y$ is a propositional knowledge base and $X\models Y$, in modal system $\mathcal{T}$ 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 $\Box Y$ is less than the size of the prime implicates of $X\cup\Box Y$.Comment: 20 page

An Algorithm for Computing Prime Implicates in Modal Logic Using Resolution

In this paper we have proposed an algorithm for computing prime implicates of a modal formula in $\mathbf{K}$ using resolution method suggested in \cite{Enjalbert}. The algorithm suggested in this paper takes polynomial times exponential time ,i.e, $O(n^{2k}\times 2^{n})$ to compute prime implicates whereas Binevenu's algorithm \cite{Bienvenu} takes doubly exponential time to compute prime implicates. We have also proved its correctness