{"id":2,"date":"2011-04-11T10:48:16","date_gmt":"2011-04-11T09:48:16","guid":{"rendered":"http:\/\/logica.dmi.unisa.it\/lucaspada2\/?page_id=2"},"modified":"2026-03-27T15:14:28","modified_gmt":"2026-03-27T14:14:28","slug":"research","status":"publish","type":"page","link":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/research\/","title":{"rendered":"Research interests"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>Algebraic logic and duality<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>MV-algebras and \u0141ukasiewicz logic<\/strong>, approached through algebraic semantics, categorical equivalences, and geometric representations.&nbsp;&nbsp;<\/li>\n\n\n\n<li>Broad interest in&nbsp;<strong>Stone-type dualities<\/strong>&nbsp;and \u201cconcrete\u201d duality theory as a unifying toolkit across algebra and logic.&nbsp;&nbsp;<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Algebraic structures and their representation<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Abelian lattice-ordered groups<\/strong>\u00a0(especially with strong unit) and related ordered structures, studied via representation\/duality techniques and concrete geometric models.\u00a0\u00a0<\/li>\n\n\n\n<li><strong>Commutative semirings<\/strong> (\u201crigs\u201d)\u00a0and related \u201crig geometry\u201d (structure, primes, axiomatizations, and categorical properties).\u00a0\u00a0<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Arithmetic polyhedral &amp; piecewise-linear geometry<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Piecewise linear geometry, <strong>rational polyhedra<\/strong>\u00a0and\u00a0<strong>Z-maps<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Algebraic logic and duality Algebraic structures and their representation Arithmetic polyhedral &amp; piecewise-linear geometry<\/p>\n","protected":false},"author":1,"featured_media":2366,"parent":0,"menu_order":5,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2","page","type-page","status-publish","has-post-thumbnail","hentry"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/pages\/2","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/types\/page"}],"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=2"}],"version-history":[{"count":16,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/pages\/2\/revisions"}],"predecessor-version":[{"id":2341,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/pages\/2\/revisions\/2341"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media\/2366"}],"wp:attachment":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media?parent=2"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}