conditionals

Conditionals are linguistic and logical constructs that express dependency between two propositions or events: if A occurs, then B follows. They appear across languages, sciences, and everyday reasoning, and they are studied in several disciplines, including philosophy, linguistics, computer science, and logic. In general, a conditional asserts that the truth of one part (the antecedent) has relevance for the truth or occurrence of another part (the consequent).

In logic, the conditional is a formal connective often denoted A → B. In standard propositional logic it is defined so that the statement is true whenever A is false or B is true (material implication). This can yield counterintuitive cases, such as a true conditional when A is false, even if B is false. More nuanced approaches distinguish strict or causal implications and counterfactual conditionals, which are evaluated with possible-worlds semantics or similar frameworks to capture what would be the case if A were the case.

In natural language, conditionals are typically introduced by if-clauses and can express real or hypothetical scenarios. English exemplars include the zero conditional (If you heat ice, it melts), the first conditional (If it rains, we will stay indoors), the second conditional (If I won the lottery, I would travel), and the third conditional (If I had studied, I would have passed). Mixed conditionals combine elements from different times to convey nuanced meanings. Conditionals can denote factual possibilities, hypothetical reasoning, or counterfactual thoughts, with interpretation influenced by tense, modality, and context.

Beyond language, conditionals appear in programming and artificial intelligence as constructs that direct control flow and decision-making, typically expressed as if-then statements.