On consistency and completeness of autoepistemic theories
Fundamenta Informaticae
Proceedings of the eleventh international conference on Logic programming
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Logic programming revisited: logic programs as inductive definitions
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
Uniform semantic treatment of default and autoepistemic logics
Artificial Intelligence
FO(ID) as an Extension of DL with Rules
ESWC 2009 Heraklion Proceedings of the 6th European Semantic Web Conference on The Semantic Web: Research and Applications
Logic programming for knowledge representation
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Nonmonotonic logics and their algebraic foundations
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
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ID-logic uses ideas from the field of logic programming to extend second order logic with non-monotone inductive defintions. In this work, we reformulate the semantics of this logic in terms of approximation theory, an algebraic theory which generalizes the semantics of several non-monotonic reasoning formalisms. This allows us to apply certain abstract modularity theorems, developed within the framework of approximation theory, to ID-logic. As such, we are able to offer elegant and simple proofs of generalizations of known theorems, as well as some new results.