{"type":"ScholarlyArticle","title":"The Orders of Magnitude Models as Qualitative Algebras","authors":[{"name":"Louise Travé-Massuyès","slug":"louise-trave-massuyes","given":"Louise","family":"Travé-Massuyès","affiliation":""},{"name":"Núria Piera","slug":"nuria-piera","given":"Núria","family":"Piera","affiliation":""}],"abstract":"This paper provides a unifying mathematical framework for orders of magnitude models used in Qualitative Physics . An axiomatic of the qualitative equality is provided and a general algebraic structure called qualitative algebra is defined . It is shown that the usual model (+,-,0,?} and the extended model recently introduced by Dubois and Prade are particular cases in the class of models that are generated from a partition of the real line . Any of these models can be structured as qualitative algebra. On the other hand, we characterize those qualitative algebras that are isomorphous, in a qualitative sense. Besides, it is shown that all these models can be embedded into one another as qualitative subalgebras.","doi":null,"url":"https://ijcai.org/proceedings/1989/202","pdf":"https://ijcai.org/proceedings/1989/0202.pdf","markdown":"https://ijcai.org/proceedings/1989/202.md","bibtex":"https://ijcai.org/proceedings/1989/bibtex/202","volume":{"slug":"1989","title":"Proceedings of the Eleventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1989","url":"https://ijcai.org/proceedings/1989/","year":1989,"location":"Detroit, Michigan, USA","dates":"August 20-25 1989","editors":"N. S. Sridharan","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Knowledge Representation","track":"Knowledge Representation","number":202,"pages":{"first":1261,"last":1265},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}