Polynomial time query processing in temporal deductive databases

We study conditions guaranteeing polynomial time computability of queries in temporal deductive databases. We show that if for a given set of temporal rules, the period of its least models is bounded from the above by a polynomial in the database size, then also the time to process yes-no queries (as well as to compute finite representations of all query answers) can be polynomially bounded. We present a bottom-up query processing algorithm BT that is guaranteed to terminate in polynomial time if the periods are polynomially bounded. Polynomial periodicity is our most general criterion, however it can not be directly applied. Therefore, we exhibit two weaker criteria, defining inflationary and I-periodic sets of temporal rules. We show that it can be decided whether a set of temporal rules is inflationary. I-periodicity is undecidable (as we show), but it can be closely approximated by a syntactic notion of multiseparability.