Querying Guarded Fragments via Resolution

Abstract: Answering Boolean conjunctive queries over the guarded fragment is decidable, however, as yet no practical decision procedure exists. Meanwhile, ordered resolution, as a practically oriented algorithm, is widely used in state-of-art modern theorem provers. In this paper, we devise a resolution decision procedure, which not only proves decidability of querying of the guarded fragment, but is implementable in any `off-the-shelf' resolution theorem prover with modest effort. Further, we extend the procedure to querying the loosely guarded fragment. The difficulty in querying a knowledge base of (loosely) guarded clauses is that query clauses are not guarded. We show however there are ways to reformulate query clauses into (loosely) guarded clauses either directly via the separation and splitting rules, or via performing inferences using our top-variable inference system combining with a form of dynamic renaming. Therefore, the problem of querying the (loosely) guarded fragment can be reduced to deciding the (loosely) guarded fragment and possibly irreducible query clauses, i.e., a clause that cannot derive any new conclusion. Meanwhile, our procedure yields a goal-oriented query rewriting algorithm: Before introducing datasets, one can produce a saturated clausal set $\mathcal{S}$ using given BCQs and (loosely) guarded theories. Clauses in $\mathcal{S}$ can be easily transformed first-order queries, therefore query answering over the (loosely) guarded fragment is reduced to evaluating a union of first-order queries over datasets. As far as we know, this is the first practical decision procedure for answering and rewriting Boolean conjunctive queries over the guarded fragment and the loosely guarded fragment.