Conditional Syntax Splitting for Non-monotonic Inference Operators
Jesse Heyninck, Gabriele Kern-Isberner, Thomas Meyer, Jonas Philipp Haldimann, Christoph Beierle
Abstract
Syntax splitting is a property of inductive inference operators that ensures we can restrict our attention to parts of the conditional belief base that share atoms with a given query. To apply syntax splitting, a conditional belief base needs to consist of syntactically disjoint conditionals. This requirement is often too strong in practice, as conditionals might share atoms. In this paper we introduce the concept of conditional syntax splitting, inspired by the notion of conditional independence as known from probability theory. We show that lexicographic inference and system W satisfy conditional syntax splitting, and connect conditional syntax splitting to several known properties from the literature on non-monotonic reasoning, including the drowning effect.
BibTeX
@article{Heyninck_Kern-Isberner_Meyer_Haldimann_Beierle_2023, title={Conditional Syntax Splitting for Non-monotonic Inference Operators}, volume={37}, url={https://ojs.aaai.org/index.php/AAAI/article/view/25789}, DOI={10.1609/aaai.v37i5.25789}, abstractNote={Syntax splitting is a property of inductive inference operators that ensures we can restrict our attention to parts of the conditional belief base that share atoms with a given query. To apply syntax splitting, a conditional belief base needs to consist of syntactically disjoint conditionals. This requirement is often too strong in practice, as conditionals might share atoms. In this paper we introduce the concept of conditional syntax splitting, inspired by the notion of conditional independence as known from probability theory. We show that lexicographic inference and system W satisfy conditional syntax splitting, and connect conditional syntax splitting to several known properties from the literature on non-monotonic reasoning, including the drowning effect.}, number={5}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Heyninck, Jesse and Kern-Isberner, Gabriele and Meyer, Thomas and Haldimann, Jonas Philipp and Beierle, Christoph}, year={2023}, month={Jun.}, pages={6416-6424} }