Conditional

Conditional refers to dependence on a condition or circumstance and is used across disciplines to describe what follows if something is true or occurs. It forms a core idea in logic, probability, linguistics, computer science, and everyday language.

In logic and mathematics, a conditional statement asserts that if a premise P is true, then a conclusion Q follows, often written as if P then Q or P → Q. In classical logic this is modeled by material implication, which is considered true whenever the antecedent is false or the consequent is true. The antecedent is the condition, and the consequent is what follows. Philosophers distinguish various forms of conditionals and discuss concepts such as contrapositions, necessity, and sufficiency.

In probability theory, a conditional probability P(A|B) expresses the probability of event A given that event B has occurred. It is defined as P(A ∩ B) / P(B) when P(B) > 0. Related concepts include conditional expectation and conditional distributions, which describe how random variables behave when conditioned on another event or variable.

In programming and computer science, a conditional controls the flow of execution. Most languages implement if/else constructs that execute different blocks depending on a boolean condition. A ternary conditional operator can select between two expressions based on a condition.

In linguistics, conditional sentences describe hypothetical situations and their outcomes. Common types include zero, first, second, and third conditionals, varying in tense and reality: zero expresses general truths; first real future possibilities; second unreal present; third unreal past.

Across domains, conditionals aid reasoning about dependence, causality, and contingency, shaping how statements, predictions, and actions are framed.