Implication

Implication is the relationship between the two statements of a conditional statement, called the antecedent and, called the consequent when implies .

In logic, logical consequence is a fundamental concept which is often used synonymously with implication. However, sometimes the term is used to distinguish between:

• Logical implication, (also implication or entailment, or the consequence relation), a relation between statements when one implies the other ; and
• Material implication, (also material conditional, conditional or conditional implication), a logical connective and binary truth function.

• In propositional logic, material implication is a valid rule of replacement which is an instance of the connective of the same name. It is the rule that states that " implies " is logically equivalent to "not- or ".

• Definitional implication -- when one statement implies another by definition. ("If Jerry is my father, then he is my son's grandfather.")
• Causal implication -- when the relation between the antecedent and consequent is discovered empirically. ("If I put the litmus paper in acid, it will turn red.")
• Decisional implication -- when there is no logical connection nor one by definition between the consequent and antecedent. This is a decision of the speaker to behave in the specified way under the specified circumstances. ("If I'm wrong, I'll eat my hat.")

Other uses:

• In modal logic, strict implication, (also strict conditional) is a modal connector, a logical connective of modal logic that expresses necessity.
• In linguistics, specifically in pragmatics:

• Implicature
• Entailment (pragmatics)

• In medical diagnosis, the scientific method, and forensics, a hypothetical cause is implicated or indicated when a reason for the condition can be found, given that cause.