Fixpoint Semantics for DatalogMTL with Negation

Abstract

DatalogMTL with negation is an extension of Datalog with metric temporal operators enriched with unstratifiable negation. In this paper, we define the stable, well-founded, Kripke-Kleene, and supported model semantics for DatalogMTL with negation in a very simple and straightforward way, by using the solid mathematical formalism of Approximation Fixpoint Theory (AFT). Moreover, we prove that the stable model semantics obtained via AFT coincides with the one defined in previous work, through the employment of pairs of interpretations stemming from the logic of here-and-there.