2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100133It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be constructed by incrementally constructing models for each level. Similar results exist for other non-monotonic formalisms, such as auto-epistemic logic and default logic. In this work, we present a general, algebraicsplitting theory for logics with a fixpoint semantics. Together with the framework of approximation theory, a general fixpoint theory for arbitrary operators, this gives us a uniform and powerful way of deriving splitting results for each logic with a fixpoint semantics. We demonstrate the usefulness of these results, by generalizing existing results for logic programming, auto-epistemic logic and default logic.Revised to correct a substantial error in Section 4.2.2 (certain results which only hold for_consistent_ possible world sets were stated to hold in general)Artificial IntelligenceLogic in Computer ScienceI.2.3; I.2.4text