Rule Consequent

A rule consequent is a logic statement within a conditional logic rule that must be true if the rule antecedent is satisfied.

• AKA: Consequent, Consequent Statement.
• Example(s):
  • "If a substance is heated to 100 degrees Celsius, then it will boil." - "it will boil" is the consequence.
  • "If it rains tomorrow, then the picnic will be canceled." - "the picnic will be cancelled" is the consequence.
  • "If a student studies diligently, then they will achieve high grades." - "They will achieve better" is the consequence.
  • "If all humans are mortal, and Socrates is a human, then Socrates is mortal." - "Socrates is mortal" is the consequence.
  • …
• Counter-Example(s)
  • a Rule Antecedent.
  • a Rule of Inference, such as Modus Tollens.
• See: Outcome, Intended Outcome, Hypothetical Proposition, Conjecture, Necessity and Sufficiency.

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References

2024

• (Wikipedia, 2024) ⇒ https://en.wikipedia.org/wiki/Consequent Retrieved:2024-8-3.
  • A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if P implies Q, then P is called the antecedent and Q is called the consequent. In some contexts, the consequent is called the apodosis.

    Examples:

    • If [math]\displaystyle{ P }[/math] , then [math]\displaystyle{ Q }[/math] . [math]\displaystyle{ Q }[/math] is the consequent of this hypothetical proposition.
    • If [math]\displaystyle{ X }[/math] is a mammal, then [math]\displaystyle{ X }[/math] is an animal.
  • Here, " [math]\displaystyle{ X }[/math] is an animal" is the consequent.
    • If computers can think, then they are alive.
  • "They are alive" is the consequent.

    The consequent in a hypothetical proposition is not necessarily a consequence of the antecedent.

    • If monkeys are purple, then fish speak Klingon.
  • "Fish speak Klingon" is the consequent here, but intuitively is not a consequence of (nor does it have anything to do with) the claim made in the antecedent that "monkeys are purple.

2015a

• (University of Kentucky, 2025) ⇒ www.uky.edu/~rosdatte/phi120/glossary.htm
  • consequent: The consequent follows the "then" in a conditional statement. Its realization is conditional upon the antecedent.

2015b

• (CYC Glossary, 2015) ⇒ http://www.cyc.com/cycdoc/ref/glossary.html
  • consequent: The consequent of a rule is its right-hand side, that is, the second argument to the #$implies connective with which the rule begins. Intuitively, every rule states that if the antecedent is true, then the consequent is true.

2015c

• (DMS, 2015) ⇒ http://dms.irb.hr/tutorial/tut_glosary.php
  • consequent (right-hand side of the rule)

    When an association between two variables is defined, the second item (or right-hand side) is called the consequent. For example, in the relationship "When a customer buys a beer, he also buys chips 25% of the time" "buys chips" is the consequent.

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