An Algebraic Account of Modularity in ID-Logic

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 certract 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.

• Type: Conference
• Year: 2005
• Where: LPNMR
• Authors: Joost Vennekens, Marc Denecker
• Keywords: Approximation Theory, LPNMR 2005, Non-monotone Inductive Defintions, Non-monotonic Reasoning Formalisms