A Compositional Semantics for 'If Then' Conditionals

In Maxime Amblard, Philippe de Groote, Sylvain Pogodalla & Christian Retoré (eds.), Logical Aspects of Computational Linguistics. Celebrating 20 Years of LACL (1996–2016). Springer. pp. 291-307 (2016)

Authors
Mathieu Vidal
Institut Jean Nicod
Abstract
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.
Keywords Conditional Logic  If  Then  Contraposition
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An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - Bulletin of Symbolic Logic 14 (4):544-545.
Elements of Symbolic Logic.Hans Reichenbach - 1947 - London: Dover Publications.

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