Recipe
Symbolize an if-then sentence
Use when: a sentence sets up a condition and a result with “if,” “provided that,” “when,” or “whenever,” in either order
Goal: a conditional with the condition before the arrow and the result after it
Taught in The conditional
Quick recipe
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1
Underline the clause attached to "if," "provided that," "when," or "whenever." That clause is the antecedent, wherever it sits in the sentence.
Example
In "The alarm sounds if the door opens," the clause attached to "if" is "the door opens."
Why: the condition is set by the word "if," not by word order.
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2
The other clause is the consequent: what the sentence promises when the condition holds.
Example
"The alarm sounds" is the result.
Why: a conditional has only two parts, so once the condition is found the rest is the result.
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3
Give each atomic claim a letter for its positive version, and build any "not" with \neg.
Example
D: The door opens. A: The alarm sounds.
Why: positive letters keep clashing claims visibly related.
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4
Write the antecedent, then \to, then the consequent. Bracket any part that uses \wedge or \vee.
Example
D \to A. With a two-part condition, "if the door opens and the system is armed" becomes (D \wedge S) \to A.
Why: the arrow points from condition to result, and brackets keep a two-part condition together.
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5
Read the formula aloud as "if …, then …" and compare it with the original sentence. Check the one breaking situation: condition true, result false.
Example
"If the door opens, then the alarm sounds." It's broken only by an opened door and a silent alarm. That is the case the English rules out.
Why: reading back catches a reversed arrow, the most common error.
Common mistakes
- Putting whichever clause comes first before the arrow.
- Writing the converse, result before condition.
- Forgetting brackets around a two-part condition.
- Treating "only if" or "unless" as a plain "if." Both reverse or change the arrow; the translation chapter covers them.