Splitting an operator: Algebraic modularity results for logics with fixpoint semantics
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It 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)
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)