Soft Computing and Its Applications, Volume One

Fuzzy Logic 253

TYPICAL PROPOSITIONAL INFERENCE RULES

Let p, .q,. and r be 3 propositions.

The following 3 propositional inference rules are commonly used for logical in-

ferencing:.

• Modus Ponens: Given a proposition p and a propositional implication rule , we

can derive the inference q. Symbolically:.

p ∧ (p → q)→q (3.18)

This above inference rule is well known as modus ponens.

• Modus Tollens: Given a proposition ~q, and the implication rule , we can de-

rive the inference ~p.

Symbolically:,

~q ∧ (p → q)→~p (3.19)

The above inference rule is known as modus tollens.

• Hypothetical Syllogism: Given two implication rules and , then we can easily ...