{"type":"ScholarlyArticle","title":"Polynomial-Time Relational Probabilistic Inference in Open Universes","authors":[{"name":"Luise Ge","slug":"luise-ge","given":"Luise","family":"Ge","affiliation":""},{"name":"Brendan Juba","slug":"brendan-juba","given":"Brendan","family":"Juba","affiliation":""},{"name":"Kris Nilsson","slug":"kris-nilsson","given":"Kris","family":"Nilsson","affiliation":""}],"abstract":"Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational problem posed by reasoning. Inspired by human reasoning, we introduce a method of first-order relational probabilistic inference that satisfies both criteria, and can handle hybrid (discrete and continuous) variables. Specifically, we extend sum-of-squares logic of expectation to relational settings, demonstrating that lifted reasoning in the bounded-degree fragment for knowledge bases of bounded quantifier rank can be performed in polynomial time, even with an a priori unknown and/or countably infinite set of objects. Crucially, our notion of tractability is framed in proof-theoretic terms, which extends beyond the syntactic properties of the language or queries.  We are able to derive the tightest bounds provable by proofs of a given degree and size and establish completeness in our sum-of-squares refutations for fixed degrees.","doi":"10.24963/ijcai.2025/1007","url":"https://ijcai.org/proceedings/2025/1007","pdf":"https://ijcai.org/proceedings/2025/1007.pdf","markdown":"https://ijcai.org/proceedings/2025/1007.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/1007","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Uncertainty in AI","track":"Main Track","number":1007,"pages":{"first":9058,"last":9067},"keywords":["Uncertainty in AI: UAI: Statistical relational AI","Uncertainty in AI: UAI: Tractable probabilistic models"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}