Splitting an operator: Algebraic modularity results for logics with fixpoint semantics
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 nonmonotonic formalisms, such as autoepistemic 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, autoepistemic logic and default logic.
 Publication:

arXiv eprints
 Pub Date:
 May 2004
 arXiv:
 arXiv:cs/0405002
 Bibcode:
 2004cs........5002V
 Keywords:

 Computer Science  Artificial Intelligence;
 Computer Science  Logic in Computer Science;
 I.2.3;
 I.2.4
 EPrint:
 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)