{"id":9280,"date":"2025-10-17T20:23:21","date_gmt":"2025-10-17T11:23:21","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9280"},"modified":"2025-10-20T18:49:21","modified_gmt":"2025-10-20T09:49:21","slug":"ch16-inference-rule-first-order-logic","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-mathematical-logic\/ch16-inference-rule-first-order-logic\/","title":{"rendered":"\uc77c\uacc4\ub17c\ub9ac\uc758 \ucd94\ub860\uaddc\uce59"},"content":{"rendered":"<div class=\"mathlogic2025\"><!-- ################## --><\/p>\n<p><!-- \n\n<h2>16. \uc77c\uacc4\ub17c\ub9ac\uc758 \ucd94\ub860\uaddc\uce59<\/h2>\n\n --><\/p>\n<p>\uc77c\uacc4\ub17c\ub9ac\uc758 \ud615\uc2dd\uacc4\ub294 \uba85\uc81c\ub17c\ub9ac\uc640 \ub9c8\ucc2c\uac00\uc9c0\ub85c <span class=\"defined\">\uc54c\ud30c\ubcb3<\/span>, <span class=\"defined\">\uacf5\ub9ac<\/span>, <span class=\"defined\">\ucd94\ub860\uaddc\uce59<\/span>\uc73c\ub85c \uad6c\uc131\ub41c\ub2e4. \uadf8\ub7ec\ub098 \uc77c\uacc4\ub17c\ub9ac\uc758 \uacf5\ub9ac\uc640 \ucd94\ub860\uaddc\uce59\uc740 \uba85\uc81c\ub17c\ub9ac\ubcf4\ub2e4 \ub354 \ubcf5\uc7a1\ud558\ub2e4.<\/p>\n<h3>\uc77c\uacc4\ub17c\ub9ac\uc758 \uacf5\ub9ac\uc640 \ucd94\ub860\uaddc\uce59<\/h3>\n<p>\uc77c\uacc4\ub17c\ub9ac\uc5d0\uc11c\ub294 \uacb0\ud569\uc790\uc640 \ud55c\uc815\uae30\ud638\ub97c \ub2e4\uc74c \uc138 \uac1c\uc758 \uae30\ud638\ub85c \ud45c\ud604\ud560 \uc218 \uc788\ub2e4.<br \/>\n\\[\\lnot, \\,\\,\\, \\rightarrow, \\,\\,\\, \\forall\\]<\/p>\n<p>\uc77c\uacc4\ub17c\ub9ac\uc758 \uacf5\ub9ac\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uc544\ud649 \uac1c\uc758 \uacf5\ub9ac\ud2c0\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\n<ul>\n<li>(A1) \\((\\phi\\rightarrow (\\psi \\rightarrow \\phi))\\)<\/li>\n<li>(A2) \\(((\\phi\\rightarrow (\\psi \\rightarrow \\theta)) \\rightarrow ((\\phi \\rightarrow \\psi)\\rightarrow (\\phi \\rightarrow \\theta)))\\)<\/li>\n<li>(A3) \\((((\\lnot \\phi) \\rightarrow (\\lnot \\phi)) \\rightarrow (\\psi \\rightarrow \\phi))\\)<\/li>\n<li>(A4) \\(((\\forall x)\\phi \\rightarrow \\phi[t\/x])\\)<\/li>\n<li>(A5) \\(x\\)\uac00 \\(\\phi\\)\uc5d0\uc11c \uc790\uc720\ubcc0\uc218\uac00 \uc544\ub2d0 \ub54c \\(((\\forall x)(\\phi \\rightarrow \\psi)\\rightarrow (\\phi \\rightarrow (\\forall x)\\psi))\\)<\/li>\n<li>(E1) \\(t\\)\uac00 \ud56d\uc77c \ub54c \\((t=t)\\)<\/li>\n<li>(E2) \\(t,\\) \\(u\\)\uac00 \ud56d\uc77c \ub54c \\(((t=u) \\rightarrow (u=t))\\)<\/li>\n<li>(E3) \\(t,\\) \\(u,\\) \\(v\\)\uac00 \ud56d\uc77c \ub54c \\(((t=u) \\rightarrow ((u=v) \\rightarrow (t=v)))\\)<\/li>\n<li>(E4) \\(((t=u) \\rightarrow (\\phi[t\/x,\\,t\/y]\\rightarrow \\phi[t\/x,\\,u\/y]))\\)<\/li>\n<\/ul>\n<p>\uc704 \uacf5\ub9ac\uc5d0\uc11c \\(\\phi[t\/x]\\)\ub294 \ub17c\ub9ac\uc2dd \\(\\phi\\)\uc5d0 \ub098\ud0c0\ub098\ub294 \uc790\uc720\ubcc0\uc218 \\(x\\)\ub97c \\(t\\)\ub85c \uce58\ud658\ud558\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/p>\n<p>\uccab \uc138 \uacf5\ub9ac(A1-A3)\ub294 \uba85\uc81c\ub17c\ub9ac\uc758 \uacf5\ub9ac\uc640 \ub3d9\uc77c\ud558\ub2e4. A4\uc640 A5\ub294 \ud55c\uc815\uae30\ud638\ub97c \ub2e4\ub8e8\uae30 \uc704\ud55c \uac83\uc774\uba70, E1-E4\ub294 \ub4f1\ud638\uc758 \uc131\uc9c8\uc744 \uc815\uc758\ud55c\ub2e4.<\/p>\n<p>\uc77c\uacc4\ub17c\ub9ac\uc758 \ucd94\ub860\uaddc\uce59\uc740 \ub2e4\uc74c \ub450 \uac00\uc9c0\uac00 \uc788\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li>(R1) Modus Ponens: \\(\\phi\\)\uc640 \\(\\phi \\rightarrow \\psi\\)\ub85c\ubd80\ud130 \\(\\psi\\)\ub97c \ucd94\ub860\ud55c\ub2e4.<\/li>\n<li>(R2) \uc77c\ubc18\ud654: \\(x\\)\uac00 \ubcc0\uc218\uc77c \ub54c, \\(\\phi\\)\ub85c\ubd80\ud130 \\((\\forall x)\\phi\\)\ub97c \ucd94\ub860\ud55c\ub2e4.<\/li>\n<\/ol>\n<h3>\uc77c\uacc4\ub17c\ub9ac\uc758 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131<\/h3>\n<p>\uc77c\uacc4\ub17c\ub9ac\uc758 \uacf5\ub9ac\uc640 \ucd94\ub860\uaddc\uce59\uc744 \ubc14\ud0d5\uc73c\ub85c \uc77c\uacc4\ub17c\ub9ac\uc5d0\uc11c \uc911\uc694\ud55c \ub450 \uc815\ub9ac\ub97c \uc18c\uac1c\ud55c\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\ub9ac 16.1. (\uac74\uc804\uc131 \uc815\ub9ac)<\/span><\/p>\n<p>\ub17c\ub9ac\uc2dd \\(\\phi\\)\uac00 \uc815\ub9ac\uc774\uba74 \\(\\phi\\)\ub294 \ub17c\ub9ac\uc801\uc73c\ub85c \uc720\ud6a8\ud558\ub2e4. \ub354 \uc77c\ubc18\uc801\uc73c\ub85c, \\(\\varSigma\\)\uac00 \ub17c\ub9ac\uc2dd\uc758 \uc9d1\ud569\uc774\uace0 \\(\\phi\\)\uac00 \ub17c\ub9ac\uc2dd\uc77c \ub54c, \\(\\phi\\)\uac00 \\(\\varSigma\\)\ub85c\ubd80\ud130 \ucd94\ub860\ub420 \uc218 \uc788\uc73c\uba74 \\(\\phi\\)\ub294 \\(\\varSigma\\)\uc758 \ub17c\ub9ac\uc801 \uadc0\uacb0\uc774\ub2e4.<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofbegin\"><span class=\"proof\">\uc99d\uba85 \uac1c\uc694<\/span><br \/>\n\uac74\uc804\uc131 \uc815\ub9ac\ub294 \uacf5\ub9ac\uac00 \ubaa8\ub450 \ub17c\ub9ac\uc801\uc73c\ub85c \uc720\ud6a8\ud558\uace0, \ucd94\ub860\uaddc\uce59\uc774 \ub17c\ub9ac\uc801 \uc720\ud6a8\uc131\uc744 \ubcf4\uc874\ud55c\ub2e4\ub294 \uc0ac\uc2e4\uc5d0 \uae30\ucd08\ud55c\ub2e4. \uc99d\uba85\uc740 \\(\\varSigma\\)\ub85c\ubd80\ud130\uc758 \\(\\phi\\)\uc758 \uc99d\uba85 \uae38\uc774\uc5d0 \ub300\ud55c \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc744 \uc0ac\uc6a9\ud55c\ub2e4.<\/p>\n<p>\uae30\ubcf8 \ub2e8\uacc4: \\(\\phi\\)\uac00 \uacf5\ub9ac\uc774\uac70\ub098 \\(\\varSigma\\)\uc5d0 \uc18d\ud558\ub294 \uacbd\uc6b0, \\(\\phi\\)\uc758 \ub17c\ub9ac\uc801 \uc720\ud6a8\uc131\uc740 \uc790\uba85\ud558\ub2e4.<\/p>\n<p>\uadc0\ub0a9 \ub2e8\uacc4: \\(\\phi\\)\uac00 \ucd94\ub860\uaddc\uce59\uc744 \ud1b5\ud574 \uc5bb\uc5b4\uc9c4 \uacbd\uc6b0, \uadc0\ub0a9\uc801 \uac00\uc815\uc5d0 \uc758\ud574 \ucd94\ub860\uc5d0 \uc0ac\uc6a9\ub41c \ub17c\ub9ac\uc2dd\ub4e4\uc774 \ub17c\ub9ac\uc801\uc73c\ub85c \uc720\ud6a8\ud558\ubbc0\ub85c \\(\\phi\\) \uc5ed\uc2dc \ub17c\ub9ac\uc801\uc73c\ub85c \uc720\ud6a8\ud558\ub2e4.<span class=\"qed\"><\/span><\/p>\n<\/div>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\ub9ac 16.2. (\uc644\uc804\uc131 \uc815\ub9ac)<\/span><\/p>\n<p>\uac00\uc0b0 \uac1c\uc758 \ud568\uc218\uae30\ud638, \uad00\uacc4\uae30\ud638, \uc0c1\uc218\uae30\ud638\ub97c \uac00\uc9c4 \uc77c\uacc4\ub17c\ub9ac\uc5b8\uc5b4 \\(\\mathcal{L}\\)\uc5d0 \ub300\ud574, \ub17c\ub9ac\uc2dd \\(\\phi\\)\uac00 \ub17c\ub9ac\uc801\uc73c\ub85c \uc720\ud6a8\ud558\uba74 \\(\\phi\\)\ub294 \uc815\ub9ac\uc774\ub2e4. \ub354 \uc77c\ubc18\uc801\uc73c\ub85c, \\(\\varSigma\\)\uac00 \ub17c\ub9ac\uc2dd\uc758 \uc9d1\ud569\uc774\uace0 \\(\\phi\\)\uac00 \ub17c\ub9ac\uc2dd\uc77c \ub54c, \\(\\phi\\)\uac00 \\(\\varSigma\\)\uc758 \ub17c\ub9ac\uc801 \uadc0\uacb0\uc774\uba74 \\(\\phi\\)\ub294 \\(\\varSigma\\)\ub85c\ubd80\ud130 \ucd94\ub860\ub420 \uc218 \uc788\ub2e4.<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofbegin\"><span class=\"proof\">\uc99d\uba85 \uac1c\uc694<\/span><br \/>\n\uc644\uc804\uc131 \uc815\ub9ac\ub294 \ub354 \uac15\ud55c \uacb0\uacfc\uc778 &#8220;\ub17c\ub9ac\uc2dd\uc758 \uc9d1\ud569 \\(\\varSigma\\)\uac00 \ubb34\ubaa8\uc21c\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(\\varSigma\\)\uac00 \ubaa8\ub378\uc744 \uac00\uc9c0\ub294 \uac83\uc774\ub2e4&#8221;\ub97c \uc99d\uba85\ud568\uc73c\ub85c\uc368 \uc5bb\uc744 \uc218 \uc788\ub2e4. \uc99d\uba85\uc740 \ub2e4\uc74c \ub2e8\uacc4\ub85c \uc9c4\ud589\ub41c\ub2e4.<\/p>\n<ol class=\"parenthesis\" style=\"margin-left: 3em;\">\n<li>\\(\\mathcal{L}\\)\uc5d0 \uc0c8\ub85c\uc6b4 \uc0c1\uc218\ub4e4\uc744 \ucd94\uac00\ud558\uc5ec \ud655\uc7a5\ud55c\ub2e4.<\/li>\n<li>\\(\\varSigma\\)\uac00 \ubb34\ubaa8\uc21c\uc774\uba74 \\(\\varSigma\\)\ub97c \ud3ec\ud568\ud558\ub294 \uc644\uc804\ud558\uace0 \ubb34\ubaa8\uc21c\uc778 \uc9d1\ud569 \\(\\varSigma^+\\)\uac00 \uc874\uc7ac\ud568\uc744 \ubcf4\uc778\ub2e4.<\/li>\n<li>\\(\\varSigma^+\\)\ub97c \uc0ac\uc6a9\ud558\uc5ec \ubaa8\ub378\uc744 \uad6c\uc131\ud55c\ub2e4.<\/li>\n<li>\uc774 \ubaa8\ub378\uc774 \\(\\varSigma\\)\uc758 \ubaa8\ub378\uc784\uc744 \uc99d\uba85\ud55c\ub2e4.<\/li>\n<\/ol>\n<p>\uc774\ub7ec\ud55c \ubc29\ubc95\uc744 \ud1b5\ud574 \ubb34\ubaa8\uc21c\uc778 \ub17c\ub9ac\uc2dd \uc9d1\ud569\uc774 \ubaa8\ub378\uc744 \uac00\uc9d0\uc744 \ubcf4\uc774\uace0, \uc774\uac83\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc644\uc804\uc131 \uc815\ub9ac\ub97c \uc99d\uba85\ud55c\ub2e4.<span class=\"qed\"><\/span><\/p>\n<\/div>\n<p>\uc774 \uc815\ub9ac\ub4e4\uc740 \uc77c\uacc4\ub17c\ub9ac\uc758 \uad6c\ubb38\ub860\uacfc \uc758\ubbf8\ub860 \uc0ac\uc774\uc758 \uad00\uacc4\ub97c \uc124\uba85\ud55c\ub2e4. \uc989, \ub17c\ub9ac\uc801\uc73c\ub85c \uc720\ud6a8\ud55c \uac83\uacfc \ud615\uc2dd\uc801\uc73c\ub85c \uc99d\uba85 \uac00\ub2a5\ud55c \uac83\uc774 \uc77c\uce58\ud55c\ub2e4\ub294 \uac83\uc744 \ubcf4\uc5ec\uc900\ub2e4.<\/p>\n<div class=\"contentbottombox\">\n<p class=\"contentbottomboxtitle\"><a href=\"\/blog\/invitation-to-mathematical-logic\/\">\uc9d1\ud569\uacfc \uc218\ub9ac\ub17c\ub9ac \uccab\uac78\uc74c \ubaa9\ucc28 \ubcf4\uae30<\/a><\/p>\n<p><span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch01-naive-logic\/\">\uba85\uc81c\uc640 \ub17c\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch02-sets\">\uc9d1\ud569\uc758 \uac1c\ub150<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch03-algebra-of-classes\">\ub2e4\uc591\ud55c \uc9d1\ud569\uc758 \uc5f0\uc0b0<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch04-relations-and-functions\">\uad00\uacc4\uc640 \ud568\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch05-infinite-sets\">\uc720\ud55c\uc9d1\ud569\uacfc \ubb34\ud55c\uc9d1\ud569<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch06-natural-numbers\">\uc790\uc5f0\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch07-cardinal-numbers\">\uc9d1\ud569\uc758 \uae30\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch08-ordinal-numbers\">\uc9d1\ud569\uc758 \uc11c\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch09-axiomatic-set-theory\">\uc9d1\ud569\ub860\uc758 \uacf5\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch10-axiom-of-choice\">\uc120\ud0dd \uacf5\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch11-formal-logic\">\ud615\uc2dd\ub17c\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch12-propositional-logic\">\uba85\uc81c\ub17c\ub9ac\uc758 \uac1c\ub150<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch13-soundness-completeness-proplogic\">\uba85\uc81c\ub17c\ub9ac\uc758 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch14-syntax-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \uad6c\ubb38\ub860<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch15-semantics-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \uc758\ubbf8\ub860<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch16-inference-rule-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \ucd94\ub860\uaddc\uce59<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch17-compactness-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \ucf64\ud329\ud2b8\uc131<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch18-peano-arithmetics\">\ud398\uc544\ub178 \uc0b0\uc220<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch19-incompleteness-theorem\">\ubd88\uc644\uc804\uc131 \uc815\ub9ac<\/a><\/span>\n<\/div>\n<\/div>\n<p><!-- ################## --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc77c\uacc4\ub17c\ub9ac\uc758 \ud615\uc2dd\uacc4\ub294 \uba85\uc81c\ub17c\ub9ac\uc640 \ub9c8\ucc2c\uac00\uc9c0\ub85c \uc54c\ud30c\ubcb3, \uacf5\ub9ac, \ucd94\ub860\uaddc\uce59\uc73c\ub85c \uad6c\uc131\ub41c\ub2e4. \uadf8\ub7ec\ub098 \uc77c\uacc4\ub17c\ub9ac\uc758 \uacf5\ub9ac\uc640 \ucd94\ub860\uaddc\uce59\uc740 \uba85\uc81c\ub17c\ub9ac\ubcf4\ub2e4 \ub354 \ubcf5\uc7a1\ud558\ub2e4. \uc77c\uacc4\ub17c\ub9ac\uc758 \uacf5\ub9ac\uc640 \ucd94\ub860\uaddc\uce59 \uc77c\uacc4\ub17c\ub9ac\uc5d0\uc11c\ub294 \uacb0\ud569\uc790\uc640 \ud55c\uc815\uae30\ud638\ub97c \ub2e4\uc74c \uc138 \uac1c\uc758 \uae30\ud638\ub85c \ud45c\ud604\ud560 \uc218 \uc788\ub2e4. \\(\\lnot, \\,\\,\\, \\rightarrow, \\,\\,\\, \\forall\\) \uc77c\uacc4\ub17c\ub9ac\uc758 \uacf5\ub9ac\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uc544\ud649 \uac1c\uc758 \uacf5\ub9ac\ud2c0\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. (A1) \\((\\phi\\rightarrow (\\psi \\rightarrow \\phi))\\) (A2) \\(((\\phi\\rightarrow (\\psi \\rightarrow \\theta)) \\rightarrow ((\\phi \\rightarrow \\psi)\\rightarrow (\\phi \\rightarrow \\theta)))\\) (A3) \\((((\\lnot \\phi) \\rightarrow (\\lnot&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9246,"menu_order":116,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-9280","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9280","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=9280"}],"version-history":[{"count":14,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9280\/revisions"}],"predecessor-version":[{"id":9447,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9280\/revisions\/9447"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9246"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=9280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}