Antecedent (logic)

An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called the protasis.

Examples:


 * If $$P$$, then $$Q$$.

This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q. In the implication "$$\phi$$ implies $$\psi$$", $$\phi$$ is called the antecedent and $$\psi$$ is called the consequent. Antecedent and consequent are connected via logical connective to form a proposition.


 * If $$X$$ is a man, then $$X$$ is mortal.

"$$X$$ is a man" is the antecedent for this proposition while "$$X$$ is mortal" is the consequent of the proposition.


 * If men have walked on the Moon, then I am the king of France.

Here, "men have walked on the Moon" is the antecedent and "I am the king of France" is the consequent.

Let $$y=x+1$$.


 * If $$x=1$$ then $$y=2$$,.

"$$x=1$$" is the antecedent and "$$y=2$$" is the consequent of this hypothetical proposition.