{"type":"ScholarlyArticle","title":"Reasoning about Probabilities in Unbounded First-Order Dynamical Domains","authors":[{"name":"Vaishak Belle","slug":"vaishak-belle","given":"Vaishak","family":"Belle","affiliation":"University of Edinburgh United Kingdom"},{"name":"Gerhard Lakemeyer","slug":"gerhard-lakemeyer","given":"Gerhard","family":"Lakemeyer","affiliation":"† Also affiliated with the University of Toronto , Canada.; RWTH Aachen University Germany"}],"abstract":"When it comes to robotic agents operating in an uncertain world, a major concern in knowledge representation  is to better relate high-level logical accounts of belief and action to the low-level probabilistic sensorimotor data. Perhaps the most general formalism for dealing with degrees of belief and, in particular, how such beliefs should evolve in the presence of noisy sensing and acting is the account  by Bacchus, Halpern, and Levesque. \r\n\r\nIn this paper, we reconsider that model of belief, and propose a new logical variant that has much of the expressive power of the original, but goes beyond it in novel ways. In particular, by moving to a semantical account of a modal variant of the situation calculus based on possible worlds with unbounded domains and probabilistic distributions over them, we are able to capture the beliefs of a fully introspective knowledge base with uncertainty by way of an only-believing operator. The paper introduces the new logic and discusses key properties as well as examples that demonstrate how the beliefs of a knowledge base change as a result of noisy actions.","doi":"10.24963/ijcai.2017/115","url":"https://ijcai.org/proceedings/2017/115","pdf":"https://ijcai.org/proceedings/2017/0115.pdf","markdown":"https://ijcai.org/proceedings/2017/115.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/115","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Knowledge Representation, Reasoning, and Logic","track":"Main track","number":115,"pages":{"first":828,"last":836},"keywords":["Uncertainty in AI: Uncertainty Representations","Knowledge Representation, Reasoning, and Logic: Reasoning about Knowlege and Belief","Knowledge Representation, Reasoning, and Logic: Action, Change and Causality","Uncertainty in AI: Uncertainty in AI"],"videos":[],"references":[{"position":1,"raw":"[Aumann, 1999] R. 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