# inference rule

## inference rule

(logic)A procedure which combines known facts to produce
("infer") new facts. For example, given that

1. Socrates is a man and that 2. all men are motal,

we can infer that Socrates is mortal. This uses the rule known as "modus ponens" which can be written in Boolean algebra as

(A & A => B) => B

(if proposition A is true, and A implies B, then B is true).

Or given that,

1. Either Denis is programming or Denis is sad and 2. Denis is not sad,

we can infer that Denis is programming. This rule can be written

((A OR B) & not B) => A

(If either A is true or B is true (or both), and B is false, then A must be true).

1. Socrates is a man and that 2. all men are motal,

we can infer that Socrates is mortal. This uses the rule known as "modus ponens" which can be written in Boolean algebra as

(A & A => B) => B

(if proposition A is true, and A implies B, then B is true).

Or given that,

1. Either Denis is programming or Denis is sad and 2. Denis is not sad,

we can infer that Denis is programming. This rule can be written

((A OR B) & not B) => A

(If either A is true or B is true (or both), and B is false, then A must be true).

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