Abstract
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, algebraic splitting theory for programs/theories under 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 Lifschitz and Turner’s splitting theorem to other semantics for (non-disjunctive) logic programs.
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Vennekens, J., Gilis, D., Denecker, M. (2004). Splitting an Operator. In: Demoen, B., Lifschitz, V. (eds) Logic Programming. ICLP 2004. Lecture Notes in Computer Science, vol 3132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27775-0_14
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DOI: https://doi.org/10.1007/978-3-540-27775-0_14
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