Total and Partial Well-Founded Datalog Coincide
We show that the expressive power of well-founded Datalog does not
decrease when restricted to total programs (it is known to decrease
from $\Pi_1^1$ to $\Delta_1^1$ 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
win(X) <- move(X, Y), not
win(Y)
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.
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