{"type":"ScholarlyArticle","title":"On the Decidability of Formulae Involving Continuous and Closed Functions","authors":[{"name":"Domenico Cantone","slug":"domenico-cantone","given":"Domenico","family":"Cantone","affiliation":""},{"name":"Eugenio G. Omodeo","slug":"eugenio-g-omodeo","given":"Eugenio G.","family":"Omodeo","affiliation":""}],"abstract":"The satisfiability problem for a syllogistic embracing E, \\, Boolean set operations, the Kurato~ski topological closure operation -, and contmuous and closed maps between topological spaces, along with the operations of point evaluation , set image, and inverse set image, is solved for formulae that meet a particular syntactic non-circularity property. The unquantified interpreted language £ 2 • 00 to be considered has infinitely many sorts of variables, each corresponding to a different topological space. Three kinds of variables are available, namely, individual, set, and map variables. Individual variables of a given sort are supposed to range over the universe of that sort , whereas set variables range over the subsets of t~e appropriate universe. Finally , each map vanable ranges over the collection of continuous or closed maps between two appropriate topological spaces.","doi":null,"url":"https://ijcai.org/proceedings/1989/68","pdf":"https://ijcai.org/proceedings/1989/0068.pdf","markdown":"https://ijcai.org/proceedings/1989/68.md","bibtex":"https://ijcai.org/proceedings/1989/bibtex/68","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":"Automated Deduction","track":"Automated Deduction","number":68,"pages":{"first":425,"last":429},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}