# Rule Antecedent Statement

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A Rule Antecedent Statement is a logic sentence that can be referenced by a conditional logic rule that needs to be satisfied for the rule consequent for a rule activation.

## References

### 2024

• (Wikipedia, 2024) ⇒ https://en.wikipedia.org/wiki/Antecedent_(logic) Retrieved:2024-7-27.
• 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. [1] Examples: * If $\displaystyle{ P }$ , then $\displaystyle{ Q }$ . This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q. In the implication " $\displaystyle{ \phi }$ implies $\displaystyle{ \psi }$ ", $\displaystyle{ \phi }$ is called the antecedent and $\displaystyle{ \psi }$ is called the consequent. [2] Antecedent and consequent are connected via logical connective to form a proposition.
• If $\displaystyle{ X }$ is a man, then $\displaystyle{ X }$ is mortal.
• " $\displaystyle{ X }$ is a man" is the antecedent for this proposition while " $\displaystyle{ X }$ 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 $\displaystyle{ y=x+1 }$ .

• If $\displaystyle{ x=1 }$ then $\displaystyle{ y=2 }$ ,.
• " $\displaystyle{ x=1 }$ " is the antecedent and " $\displaystyle{ y=2 }$ " is the consequent of this hypothetical proposition.
1. Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004

### 2009b

• (CYC Glossary, 2009) ⇒ http://www.cyc.com/cycdoc/ref/glossary.html
• antecedent: The antecedent of a rule is its left-hand side, that is, the first argument to the #\$implies connective with which the rule begins. Intuitively, every rule states that if the antecedent is true, then the consequent must be true.