Splitting an Operator: Algebraic Modularity Results for Logics with Fixpoint Semantics

Title: Splitting an Operator: Algebraic Modularity Results for Logics with Fixpoint Semantics

Research Question: Can logics with fixpoint semantics be split into different levels, allowing for incremental construction of models?

Methodology: The authors propose a general, algebraic splitting theory for logics with fixpoint semantics. This theory is based on approximation theory, a method that allows for the incremental construction of models. The authors demonstrate the usefulness of this theory by generalizing existing results for logic programming, auto-epistemic logic, and default logic.

Results: The authors present a general framework that allows for the splitting of logics with fixpoint semantics. They show that this framework can be used to derive splitting results for each logic with a fixpoint semantics.

Implications: The results of this research have several implications. First, it provides a better understanding of the semantics of logics with fixpoint semantics. Second, it offers a practical approach to knowledge representation, allowing for the incremental construction of models. Finally, it contributes to the development of more efficient reasoning mechanisms in artificial intelligence.

Link to Article: https://arxiv.org/abs/0405002v2 Authors: arXiv ID: 0405002v2