{"id":204,"date":"2011-10-11T13:31:27","date_gmt":"2011-10-11T11:31:27","guid":{"rendered":"http:\/\/logica.dmi.unisa.it\/lucaspada\/?p=204"},"modified":"2017-10-05T09:50:43","modified_gmt":"2017-10-05T08:50:43","slug":"advances-in-the-theory-of-mulpi-algebras","status":"publish","type":"post","link":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/204-advances-in-the-theory-of-mulpi-algebras\/","title":{"rendered":"Advances in the theory of muLPi algebras"},"content":{"rendered":"<p>Recently an expansion of <span class=\"wp-katex-eq\" data-display=\"false\">\\rm L {\\rm\\Pi\\frac{1}{2}}<\/span> logic with fixed points has <a title=\"L\u03a0 logic with fixed points\" href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/publication\/l%cf%80-logic-with-fixed-points\/\">been considered<\/a>. In the present work we study the algebraic semantics of this logic, namely <span class=\"wp-katex-eq\" data-display=\"false\">\\mu L\\Pi<\/span> algebras, from algebraic, model theoretic and computational standpoints.<br \/>\nWe provide a characterisation of free\u00a0<span class=\"wp-katex-eq\" data-display=\"false\">\\mu L\\Pi<\/span> algebras as a family of particular functions from <span class=\"wp-katex-eq\" data-display=\"false\">[0,1]^{n}<\/span> to <span class=\"wp-katex-eq\" data-display=\"false\">[0,1]<\/span>. \u00a0We show that the first-order theory of linearly ordered <span class=\"wp-katex-eq\" data-display=\"false\">\\mu L\\Pi<\/span>-algebras enjoys quantifier elimination, being, more precisely, the model completion of the theory of linearly ordered <span class=\"wp-katex-eq\" data-display=\"false\">\\rm L {\\rm\\Pi\\frac{1}{2}}<\/span> algebras. Furthermore, we give a functional representation of any <span class=\"wp-katex-eq\" data-display=\"false\">\\rm L {\\rm\\Pi\\frac{1}{2}}<\/span> algebra in the style of Di Nola Theorem for MV-algebras and finally we prove that the equational theory of <span class=\"wp-katex-eq\" data-display=\"false\">\\mu L\\Pi<\/span> algebras is in PSPACE.<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/Final-Pre-proof.pdf\">Advances in the theory of muLPi algebras<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Recently an expansion of logic with fixed points has been considered. In the present work we study the algebraic semantics of this logic, namely algebras, from algebraic, model theoretic and computational standpoints. We provide a characterisation of free\u00a0 algebras as a family of particular functions from to . \u00a0We show that the first-order theory of [&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":[67,64,66,65],"class_list":["post-204","post","type-post","status-publish","format-standard","hentry","category-preprint","tag-computational-complexity","tag-free-algebra","tag-real-closed-field","tag-l-algebras"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/204","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=204"}],"version-history":[{"count":9,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/204\/revisions"}],"predecessor-version":[{"id":1161,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/204\/revisions\/1161"}],"wp:attachment":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media?parent=204"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/categories?post=204"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/tags?post=204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}