{"type":"ScholarlyArticle","title":"A Fuzzy Modal Logic for Belief Functions","authors":[{"name":"Lluís Godo","slug":"lluis-godo","given":"Lluís","family":"Godo","affiliation":""},{"name":"Petr Hájek","slug":"petr-hajek","given":"Petr","family":"Hájek","affiliation":""},{"name":"Francesc Esteva","slug":"francesc-esteva","given":"Francesc","family":"Esteva","affiliation":""}],"abstract":"In this paper we introduce a new logical approach to reason explicitly about Dempster-Shafer belief functions. We adopt the following view: one just starts with Boolean formulas and a belief function on them; the belief of is taken to be the truth degree of the (fuzzy) proposition \u0001 standing for “is believed”. For our complete axiomatization (Hylbert-style) we use one of the possible definitions of belief, namely as probability of (modal) necessity. This enables us to define a logical system combining the modal logic S5 with an already proposed fuzzy logic approach to reason about probabilities. In particular, our fuzzy logic is the logic Ł\u0002 \u0003 \u0004 which puts Lukasiewicz and Product logics together.","doi":null,"url":"https://ijcai.org/proceedings/2001/99","pdf":"https://ijcai.org/proceedings/2001/0099.pdf","markdown":"https://ijcai.org/proceedings/2001/99.md","bibtex":"https://ijcai.org/proceedings/2001/bibtex/99","volume":{"slug":"2001","title":"Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2001","url":"https://ijcai.org/proceedings/2001/","year":2001,"location":"Seattle, Washington, USA","dates":"","editors":"","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":99,"pages":{"first":723,"last":731},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}