{"id":4726,"date":"2015-01-15T08:15:01","date_gmt":"2015-01-15T07:15:01","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=4726"},"modified":"2015-01-15T08:15:01","modified_gmt":"2015-01-15T07:15:01","slug":"resena-a-mechanised-proof-of-godels-incompleteness-theorems-using-nominal-isabelle","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/resena-a-mechanised-proof-of-godels-incompleteness-theorems-using-nominal-isabelle\/","title":{"rendered":"Rese\u00f1a: A mechanised proof of G\u00f6del&#8217;s incompleteness theorems using Nominal Isabelle"},"content":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Isabelle sobre metal\u00f3gica titulado <a href=\"http:\/\/bit.ly\/14pM6gr\">A mechanised proof of G\u00f6del&#8217;s incompleteness theorems using Nominal Isabelle<\/a>.<\/p>\n<p>Su autor es <a href=\"http:\/\/www.cl.cam.ac.uk\/~lp15\">Lawrence C. Paulson<\/a> (de la Univ. de Cambridge, Inglaterra).<\/p>\n<p>Su resumen es<\/p>\n<blockquote><p>\n  An Isabelle\/HOL formalisation of G\u00f6del\u2019s two incompleteness theorems is presented. The work follows Swierczkowski\u2019s detailed proof of the theorems using <a href=\"http:\/\/journals.impan.gov.pl\/dm\/Inf\/422-0-1.html\">hereditarily finite (HF) set theory<\/a>. Avoiding the usual arithmetical encodings of syntax eliminates the necessity to formalise elementary number theory within an embedded logical calculus. The Isabelle formalisation uses two separate treatments of variable binding: the <a href=\"http:\/\/www4.in.tum.de\/~urbanc\/Publications\/nom-tech.pdf\">nominal package<\/a> is shown to scale to a development of this complexity, while <a href=\"http:\/\/bit.ly\/1AhNUBd\">de Bruijn indices<\/a> turn out to be ideal for coding syntax. Critical details of the Isabelle proof are described, in particular gaps and errors found in the literature.\n<\/p><\/blockquote>\n<p>El c\u00f3digo de las correspondientes teor\u00edas en Isabelle se encuentra <a href=\"http:\/\/bit.ly\/1sBbdbL\">aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Isabelle sobre metal\u00f3gica titulado A mechanised proof of G\u00f6del&#8217;s incompleteness theorems using Nominal Isabelle. Su autor es Lawrence C. Paulson (de la Univ. de Cambridge, Inglaterra). Su resumen es An Isabelle\/HOL formalisation of G\u00f6del\u2019s two incompleteness theorems is presented. The work follows Swierczkowski\u2019s detailed proof of&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[100],"tags":[144,285],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/4726"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/comments?post=4726"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/4726\/revisions"}],"predecessor-version":[{"id":4727,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/4726\/revisions\/4727"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=4726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=4726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=4726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}