{"id":1971,"date":"2021-04-20T11:52:29","date_gmt":"2021-04-20T09:52:29","guid":{"rendered":"http:\/\/icar.cnrs.fr\/dicoplantin\/?p=1971"},"modified":"2024-11-04T18:28:49","modified_gmt":"2024-11-04T17:28:49","slug":"relation","status":"publish","type":"post","link":"https:\/\/icar.cnrs.fr\/dicoplantin\/relation\/","title":{"rendered":"Relation"},"content":{"rendered":"

RELATION<\/strong><\/span><\/p>\n\n\n\n
En s\u00e9mantique, une relation est un pr\u00e9dicat (verbe ou locution verbale) <\/strong>\u00e0 deux places associant deux \u00eatres ou deux objets, a <\/strong>et b<\/strong>.<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Trois propri\u00e9t\u00e9s g\u00e9n\u00e9rales permettent de caract\u00e9riser les relations :<\/p>\n

\u2014\u00a0R\u00e9ciprocit\u00e9<\/em> <\/a>ou sym\u00e9trie <\/em><\/strong>: La relation qui lie a <\/strong>\u00e0 b <\/strong>lie-t-elle b <\/strong>\u00e0 a\u00a0<\/strong>?
\nConsid\u00e9rons les relations P <\/strong>\u201c\u2013 \u00eatre le p\u00e8re de \u2013<\/em>\u201d\u00a0et F <\/strong>\u201c\u2013 \u00eatre le fr\u00e8re ou la s\u0153ur de \u2013<\/em>\u201d<\/p>\n

si a<\/strong> est le p\u00e8re de b<\/strong>, b<\/strong> n’est pas le p\u00e8re de a
\n<\/strong>P<\/strong> n’est pas sym\u00e9trique<\/em><\/span><\/p>\n

si a<\/strong> est le fr\u00e8re ou la s\u0153ur de b<\/strong>, alors b<\/strong> est le fr\u00e8re ou la s\u0153ur de a
\n<\/strong>F<\/strong> est sym\u00e9trique<\/em><\/span><\/p>\n

\u2014 R\u00e9flexivit\u00e9<\/em><\/a> :<\/strong> La relation lie-t-elle\u00a0a\u00a0<\/strong>\u00e0 lui-m\u00eame ?<\/p>\n

La relation P<\/strong> n’est pas r\u00e9flexive, personne n’est son propre p\u00e8re.
\nLa relation d’\u00e9galit\u00e9 E<\/strong> \u201c\u2013 \u00eatre \u00e9gal \u00e0 \u2013<\/em>\u201d\u00a0est r\u00e9flexive\u00a0:<\/p>\n

a<\/strong> est \u00e9gal \u00e0 a<\/strong><\/span><\/p>\n

\u2014 Transitivit\u00e9<\/em><\/a>\u00a0<\/strong>: Si la relation lie a <\/strong>\u00e0 b <\/strong>et b <\/strong>\u00e0 c <\/strong>lie-t-elle a <\/strong>\u00e0 c\u00a0<\/strong>?<\/p>\n

Les ennemis de mes ennemis sont mes amis <\/em>: l’inimiti\u00e9 proverbiale n’est pas transitive,
\nSi a<\/strong> est l’ennemi de b<\/strong> et b<\/strong> l’ennemi de c, <\/strong><\/span>alors a<\/strong> est l’ami de c<\/strong>.<\/span><\/p>\n

Les amis de mes amis sont mes amis<\/em>\u00a0: l’amiti\u00e9 proverbiale est transitive,<\/span>
\nsi a<\/strong> est l’ami de b<\/strong> et b<\/strong> l’ami de c, <\/strong>alors c <\/strong>est l’ami de a<\/strong><\/span><\/p>\n

Les inf\u00e9rences fond\u00e9es sur ces propri\u00e9t\u00e9s font partie des \u00e9vidences g\u00e9n\u00e9ralement inaper\u00e7ues (faisant consensus) exploit\u00e9es par l\u2019argumentation quotidienne. Savoir jongler avec la r\u00e9ciprocit\u00e9, la r\u00e9flexivit\u00e9 et la transitivit\u00e9, c’est savoir parler sa langue, comp\u00e9tence qui sera red\u00e9finie et d\u00e9velopp\u00e9e par l’\u00e9ducation math\u00e9matique.<\/p>\n

Soit la relation de termes oppos\u00e9s corr\u00e9latifs, par exemple : \u201cm\u00e8re – fille<\/strong>\u201d. Cette relation
\n\u2014 est sym\u00e9trique : a <\/strong>est la m\u00e8re de sa fille b<\/strong> et b<\/strong> est la fille de sa m\u00e8re a<\/strong>
\n\u2014 n’est pas r\u00e9flexive : personne n’est sa propre m\u00e8re
\n\u2014 n’est pas transitive : a<\/strong> la m\u00e8re de\u00a0 b<\/strong> et b<\/strong> la m\u00e8re de c, a <\/strong>est la grand’m\u00e8re de c.<\/strong><\/p>\n

\n

\u00a0<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

RELATION En s\u00e9mantique, une relation est un pr\u00e9dicat (verbe ou locution verbale) \u00e0 deux places associant deux \u00eatres ou deux objets, a et b. Trois propri\u00e9t\u00e9s g\u00e9n\u00e9rales permettent de caract\u00e9riser les relations : \u2014\u00a0R\u00e9ciprocit\u00e9 ou sym\u00e9trie : La relation qui lie a \u00e0 b lie-t-elle b \u00e0 a\u00a0? Consid\u00e9rons les relations P \u201c\u2013 \u00eatre le […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1971","post","type-post","status-publish","format-standard","hentry","category-non-classe"],"_links":{"self":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/1971","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/comments?post=1971"}],"version-history":[{"count":14,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/1971\/revisions"}],"predecessor-version":[{"id":12375,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/1971\/revisions\/12375"}],"wp:attachment":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/media?parent=1971"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/categories?post=1971"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/tags?post=1971"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}