Follows:
What comes after, what depends on, is conditioned or caused by, or is
preceeded by something. In logic: B follows
from A if there is a valid
proof or argument
that if A is true, then B is true. Following is an extremely
general concept, and many intuitions about it
somehow involve time and
sequences. Also, the notions of
dependency,
conditoning and causing have had various
explanations and all involve some unclarities.
In any case, that suchandsuch somehow follows (probably or
certainly) from soandso is a fundamental idea or kind of fact or statement,
temporally, logically, semantically, prooftheoretically, probabilistically,
and physically, and has found various formalizations, explanations and
analyses.
The common logical kernel in the various notions of following (that may be
quite complicated) seems to be a reflexive and transitive relation conforming
to <=.
It is an interesting  technical  fact that at present (2007) there are
quite a few programs available that make or check mathematical proofs, and
also systems that are capable of some sort of
heuristical reasoning. Those who are interested in this should check the
internet, and should realize that these systems generally require some
understanding of logic, mathematics and programming (the last often in the
form of Lisp).

See also: Causation, Consequence,
Entailment,
Induction, Logic,
Logical Terms
Literature:
Adams 1 and 2, Burks, Bochenski, Gazdar, Hasenjäger, Hume, Goldblatt,
Grize, Hooker, W. Johnson, Kneale, D. Lewis, Lyons, Schopenhauer
