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The semantics of each element are first examined separately. The meaning of <jats:italic>if<\/jats:italic> is modeled according to a possible worlds semantics. The particle <jats:italic>then<\/jats:italic> is analyzed as an anaphoric word that places its focused element inside the context settled by a previous element. Their meanings are subsequently combined in order to provide a formal semantics of <jats:italic>if A then C<\/jats:italic> conditionals, which differs from the simple <jats:italic>if A, C<\/jats:italic> form. This semantics has the particularity of validating contraposition for the first type but invalidating it for the second type. Finally, a detailed examination of the sentences presented in the literature opposing this schema of reasoning shows that these counterexamples do not generally concern <jats:italic>if then<\/jats:italic> conditionals but, rather, <jats:italic>even if<\/jats:italic> conditionals and that contraposition is therefore a valid means of reasoning with regard to <jats:italic>if then<\/jats:italic> conditionals in natural language, as this system predicts.<\/jats:p>","DOI":"10.1007\/978-3-662-53826-5_18","type":"book-chapter","created":{"date-parts":[[2016,11,9]],"date-time":"2016-11-09T11:59:48Z","timestamp":1478692788000},"page":"291-307","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Compositional Semantics for \u2018If Then\u2019 Conditionals"],"prefix":"10.1007","author":[{"given":"Mathieu","family":"Vidal","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,11,10]]},"reference":[{"key":"18_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7622-2","volume-title":"The Logic of Conditionals","author":"EW Adams","year":"1975","unstructured":"Adams, E.W.: The Logic of Conditionals. 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