Total and partial well-founded datalog coincide

Abstract

We show that the expressive power of well-founded Datalog does not decrease when restricted to total programs (it is known to decrease from Π 11 to Δ 11 on infinite Herbrand structures) thereby affirmatively answering an open question posed by Abiteboul, Hull, and Vianu [AHV95]. In particular, we show that for every well-founded Datalog program there exists an equivalent total program whose only recursive rule is of the form (equation presented) where move is definable by a quantifier-free first-order formula. This yields a nice new normal form for well-founded Datalog and implies that it is sufficient to consider draw-free games in order to evaluate arbitrary Datalog programs under the well-founded semantics.