{"id":176,"date":"2011-10-11T13:03:13","date_gmt":"2011-10-11T12:03:13","guid":{"rendered":"http:\/\/logica.dmi.unisa.it\/lucaspada\/?p=176"},"modified":"2014-01-11T22:40:54","modified_gmt":"2014-01-11T21:40:54","slug":"continuous-approximations-of-mv-algebras-with-product-and-product-residuation-a-category-theoretic-equivalence","status":"publish","type":"post","link":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/176-continuous-approximations-of-mv-algebras-with-product-and-product-residuation-a-category-theoretic-equivalence\/","title":{"rendered":"Continuous approximations of MV-algebras with product and product residuation: a category-theoretic equivalence"},"content":{"rendered":"<p>A new class of $MV$-algebras with product, called L$\\Pi_q$-algebras, has been introduced. In these algebras, the discontinuous product residuation $\\to_\\pi$ \u00a0is replaced by a continuous approximation of it. These algebras seem to be a good compromise between the need ofexpressiveness and the need of continuity of connectives. \u00a0Following a good tradition in many-valued logic, in this paper we introduce a class of commutative $f$-rings with strong unit and with a sort of weak divisibility property, called $f$-quasifields, and we show that the categories of L$\\Pi_q$-algebras and of $f$-quasifields are equivalent.<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/logica.dmi.unisa.it\/lucaspada\/wp-content\/uploads\/Art.pdf\">Continuous approximations of MV-algebras with product and product residuation: a category-theoretic equivalence<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A new class of $MV$-algebras with product, called L$\\Pi_q$-algebras, has been introduced. In these algebras, the discontinuous product residuation $\\to_\\pi$ \u00a0is replaced by a continuous approximation of it. These algebras seem to be a good compromise between the need ofexpressiveness and the need of continuity of connectives. \u00a0Following a good tradition in many-valued logic, in [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[29,77],"class_list":["post-176","post","type-post","status-publish","format-standard","hentry","category-preprint","tag-mv-algebras","tag-product-logic"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/176","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/comments?post=176"}],"version-history":[{"count":2,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/176\/revisions"}],"predecessor-version":[{"id":179,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/176\/revisions\/179"}],"wp:attachment":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media?parent=176"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/categories?post=176"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/tags?post=176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}