Conditionals: Divide and Rule

Conditionals are sentences of form "if A, C". They are one of the basic elements of Logic and have many applications in Artificial Intelligence. However, their analysis is still the object of heated discussions. In this talk, we will first review the position of classical logic on this issue and its limitations. We will then look at the possible worlds approach to this problem, following Stalnaker and Lewis' works. Finally, we will present a new venue of treatment whose main idea is to classify conditional sentences into different types. This taxonomy is based on the additional syntactic markers which can be added to the main connective. We thus obtain the following list of different syntactic forms: If A, C / If A, then C / Even if A, C / Only if A, C / A if and only if C. We will show that a formal semantics based on this classification offers a more precise analysis on this issue than previous theories.