{"type":"ScholarlyArticle","title":"Asymptotic Conditional Probability in Modal Logic: A Probabilistic Reconstruction of Nonmonotonic Logic","authors":[{"name":"Riccardo Rosati","slug":"riccardo-rosati","given":"Riccardo","family":"Rosati","affiliation":""},{"name":"Georg Gottlob","slug":"georg-gottlob","given":"Georg","family":"Gottlob","affiliation":""}],"abstract":"We analyze the asymptotic conditional validity of modal formulas, i.e., the probability that a formula ψ is valid in the finite Kripke structures in which a given modal formula φ is valid, when the size of these Kripke structures grows to infinity. We characterize the formulas ψ that are almost surely valid (i.e., with probability 1) in case φ is a flat, S5consistent formula, and show that these formulas ψ are exactly those which follow from φ according to the nonmonotonic modal logic S5G. Our results provide – for the first time – a probabilistic semantics to a well-known nonmonotonic modal logic, establishing a new bridge between nonmonotonic and probabilistic reasoning, and give a computational account of the asymptotic conditional validity problem in Kripke structures.","doi":null,"url":"https://ijcai.org/proceedings/2005/185","pdf":"https://ijcai.org/proceedings/2005/0185.pdf","markdown":"https://ijcai.org/proceedings/2005/185.md","bibtex":"https://ijcai.org/proceedings/2005/bibtex/185","volume":{"slug":"2005","title":"Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2005","url":"https://ijcai.org/proceedings/2005/","year":2005,"location":"Edinburgh, Scotland, UK","dates":"","editors":"","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":185,"pages":{"first":1378,"last":1382},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}