{"type":"ScholarlyArticle","title":"A Set-Theoretic Approach to Automated Deduction in Graded Modal Logics","authors":[{"name":"Angelo Montanari","slug":"angelo-montanari","given":"Angelo","family":"Montanari","affiliation":""},{"name":"Alberto Policriti","slug":"alberto-policriti","given":"Alberto","family":"Policriti","affiliation":""}],"abstract":"In the paper, we consider the problem of supporting automated reasoning in a large class of knowledge representation formalisms, including terminological and epistemic logics, whose distinctive feature is the ability of representing and reasoning about finite quantities. Each member of this class can be represented using graded modalities, and thus the considered problem can be reduced to the problem of executing graded modal logics. We solve this problem using a set-theoretic approach that first transforms graded modal logics into polymodal logics with infinitely many modalities, and then reduces derivability in such pplymodallogics to derivability in a suitable first-order set theory.","doi":null,"url":"https://ijcai.org/proceedings/1997/30","pdf":"https://ijcai.org/proceedings/1997/0030.pdf","markdown":"https://ijcai.org/proceedings/1997/30.md","bibtex":"https://ijcai.org/proceedings/1997/bibtex/30","volume":{"slug":"1997","title":"Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1997","url":"https://ijcai.org/proceedings/1997/","year":1997,"location":"Nagoya, Japan","dates":"","editors":"Martha E. Pollack","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Automated Reasoning","track":"Automated Reasoning","number":30,"pages":{"first":196,"last":200},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}