Re: AI and Logic: Induction, Deduction, Abduction (was Re: Penrose)

Wayne Hayes (wayne@cs.toronto.edu)
Wed, 12 Nov 1997 12:18:15 -0500

I thought that my previous message might be clarified a bit if I formalized
it a bit. The formal generalization of "All men are mortal; Socrates is
a man; therefore Socrates is mortal" is

(A) for all x in the set S, property P(x) holds.
(B) y is in the set S.
(C) property P(y) holds.

The process of concluding (C) from (A) and (B) is called deduction.

The process of hypothesizing the existence of a universal law (A) from
many observations of (B) and (C) is called induction.

The process of hypothesizing (B) from the knowledge of (A) and the
observation (C) is called abduction.