{"type":"ScholarlyArticle","title":"The Complexity of Limited Belief Reasoning—The Quantifier-Free Case","authors":[{"name":"Yijia Chen","slug":"yijia-chen","given":"Yijia","family":"Chen","affiliation":"Fudan University , Shanghai 201203 , China"},{"name":"Abdallah Saffidine","slug":"abdallah-saffidine","given":"Abdallah","family":"Saffidine","affiliation":"Australian National University , Canberra ACT 2600 , Australia"},{"name":"Christoph Schwering","slug":"christoph-schwering","given":"Christoph","family":"Schwering","affiliation":"University of New South Wales , Sydney NSW 2052 , Australia"}],"abstract":"The classical view of epistemic logic is that an agent knows all the logical consequences of their knowledge base. This assumption of logical omniscience is often unrealistic and makes reasoning computationally intractable. One approach to avoid logical omniscience is to limit reasoning to a certain belief level, which intuitively measures the reasoning \"depth\".This paper investigates the computational complexity of reasoning with belief levels. First we show that while reasoning remains tractable if the level is constant, the complexity jumps to PSPACE-complete -- that is, beyond classical reasoning -- when the belief level is part of the input. Then we further refine the picture using parameterized complexity theory to investigate how the belief level and the number of non-logical symbols affect the complexity.","doi":"10.24963/ijcai.2018/245","url":"https://ijcai.org/proceedings/2018/245","pdf":"https://ijcai.org/proceedings/2018/0245.pdf","markdown":"https://ijcai.org/proceedings/2018/245.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/245","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":245,"pages":{"first":1774,"last":1780},"keywords":["Knowledge Representation and Reasoning: Reasoning about Knowlege and Belief","Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Knowledge Representation and Reasoning: Logics for Knowledge Representation","Knowledge Representation and Reasoning: Non-classical Logics for Knowledge Representation"],"videos":[],"references":[{"position":1,"raw":"[Abrahamson et al., 1995] Karl A. 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