Lecture Notes in Computer Science vol:3662 pages:291-303
8th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR) location:Diamante, Italy date:5-8 September, 2005
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, m well as some new results.