A type of speech act associated with some utterances of conditional statement. The conditional assertion corresponding to $\phi \to \psi$ is distinct from the statement that there exists an entailment relation between $\phi$ and $\psi$. Rather, the conditional assertion is interpreted as an assertion of $\psi$ with the provision that $\phi$ is true. Formal analyses of conditional assertions frequently interpret the assertoric content of a conditional assertion by the following scheme:

The assertoric content of $\phi \to \psi \text{is }\{\begin{array}{l}\psi \text{when}\phi \text{is}\text{true, and}\\ \text{nothing otherwise}\text{.}\end{array}$