A type of conditional statement in which the antecedent is phrased in the subjunctive mood, i.e., whose evaluation takes into account states of affairs that may not be actual. For example, when one asserts a counterfactual conditional, that is, a conditional of the form ‘were $\text{Φ}$ to hold then $\text{Ψ}$ would hold’ where $\text{Φ}$ is false, that $\text{Φ}$ is false in actuality does not bear on the truth of the conditional, and is determined by the properties of states (e.g., situations or possible worlds) in which $\text{Φ}$ is assumed to be true. As a consequence, the truth value of a subjunctive conditional $\phi \to \psi$ is generally regarded as not recoverable from the truth values of $\phi$ and $\psi$ alone.

Many important notions in philosophical logic have sprung from investigation of the appropriate treatment of conditionals with world semantics of this kind. For example, the introduction of logics with a strict conditional by philosopher Clarence Irving Lewis (1883–1964) was largely motivated by the feature of classical logic that, e.g., a conditional $\phi \supset \psi$ (where $\supset$ represents material implication) is true whenever $\psi$ is true. This feature suggests that the material conditional is inadequate to represent many uses of conditionals, including subjunctive conditionals. Modern semantic treatments of strict implication often employ possible worlds, corresponding to a thesis that the evaluation of subjunctive conditionals appeals to non-actual states. The closely related family of conditional logics were explicitly introduced as analyses of subjunctive conditionals, taking into account that a subjunctive conditional ‘were $\text{Φ}$ to hold then $\text{Ψ}$ would hold’ are not typically evaluated by arbitrary states of affairs at which $\text{Φ}$ is true, but by a more restricted class of states that are reasonably similar to the actual world. For example, we might consider a sentence:

• • Should one release a ball from one’s hand, it will fall to the floor.

Although a possible world at which the laws of physics fail might serve as a case in which the ball is released but does not fall, such a world is too remote to attest to the falsity of the sentence. Rather, one naturally looks to states of affairs in which the familiar laws of physics hold in order to evaluate the sentence.