🤖 AI Summary
This work addresses the lack of a unified and rigorous semantics for DatalogMTL with negation by systematically introducing Approximation Fixpoint Theory (AFT) into the language for the first time. By integrating metric temporal logic operators with non-monotonic reasoning techniques, the paper provides concise definitions of four key semantics: stable models, well-founded models, Kripke-Kleene models, and supported models. The proposed framework establishes a formally coherent and highly expressive semantic foundation. Moreover, it demonstrates that the derived stable model semantics is equivalent to the existing definition based on here-and-there temporal logic, thereby validating the effectiveness and applicability of AFT in the context of temporal logic programming.
📝 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.