entailment

In logic, entailment, also known as logical entailment or logical implication, describes a relationship where one proposition is a logical consequence of another. This means if the first proposition is true, the second must also be true.1

The propositional calculus is a system within logic that uses simple propositions as its basic units. These propositions are combined using symbols for "and" ((\cdot)), "or" ((\lor)), "if...then" ((\to)), and "not" ((\sim)). A key aspect is determining which formulas, or compound proposition forms, are provable. A formula is provable if it represents a valid inference, meaning the conclusion is always a logical consequence of the premises.2

In formal logic, material implication is often used, read as "If A, then B" ((A \to B)). This is considered false only when A is true and B is false; it's true in all other cases, regardless of the meanings of A and B. This can lead to counterintuitive results, sometimes called the "paradoxes of material implication". To address this, strict implication was introduced, requiring that it be impossible for A to be true and B to be false, focusing on the meanings of the propositions rather than just their truth values.3