Indicative conditionals: from three to four values

In this work we study how one may expand some three-valued logics of indicative conditionals by the addition of a fourth truth-value.

This is achieved through the use of twist constructions, previously introduced in the literature in order to provide algebraic semantics for these logical systems.

We first present some twist-representation results for the three-valued case, as well as for some relevant fragments and, then, we distinguish two ways of adding the new truth-value.

We also give twist-representation results for these new cases.

In the course of the paper we discuss the philosophical motivations behind the use of the new four-valued systems and some potential objections against these.