Splitting an operator: Algebraic modularity results for logics with fixpoint semantics
<|reference_start|>Splitting an operator: Algebraic modularity results for logics with fixpoint semantics: 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.<|reference_end|>
@article{vennekens2004splitting,
    title={Splitting an operator: Algebraic modularity results for logics with
  fixpoint semantics},
    author={Joost Vennekens, David Gilis, Marc Denecker},
    journal={ACM Transactions on Computational Logic, Volume 7, Number 4, 2006},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0405002},
    primaryClass={cs.AI cs.LO}
}