Chain rule for conditional arguments

Definition

The chain rule for conditional arguments allows the derivation of a conclusion from a series of conditional statements. It is used to link multiple conditionals into a single logical argument.

5 Must Know Facts For Your Next Test

1. The chain rule is often referred to as the hypothetical syllogism.
2. It is represented by the form: If P implies Q and Q implies R, then P implies R.
3. The validity of the chain rule relies on the transitive property of implications.
4. In symbolic logic, it is written as: (P → Q) ∧ (Q → R) ⊢ (P → R).
5. Understanding how to apply the chain rule can simplify complex logical arguments.

Review Questions

• What is another name for the chain rule in logic?
• How would you symbolically represent the chain rule?
• Why does the chain rule rely on the transitive property?

Related terms

Hypothetical Syllogism: A logical argument that uses two conditional statements to derive a third conditional statement.

Transitive Property: A property stating that if A implies B and B implies C, then A implies C.

Conditional Statement: A statement formed by two propositions where one proposition follows from another, typically in the form 'If P, then Q.'