This paper presents the first compositional semantics for if then conditionals. The semantics of each element are first examined separately. The meaning of if is modeled according to a possible worlds semantics. The particle then 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 if A then C conditionals, which differs from the simple if A, C 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 if then conditionals but, rather, even if conditionals and that contraposition is therefore a valid means of reasoning with regard to if then conditionals in natural language, as this system predicts. (shrink)

This paper should be read against the backdrop of three lines of linguistic investigation: the investigation of the Perfect construction, which has received considerable attention, going back to Reichenbach ; the working hypothesis that certain verbal constructions can be described in terms of the semantics of determiners on nominal expressions, with which we are more familiar; the common observation that we talk about time the way we talk about space. The focus of the paper is a particular construction in Greek. (...) As always, however, the search for the solution of a particular question reveals many other questions in the process and this paper should be seen as being also about a number of related puzzles in English and other languages. (shrink)