Induction

[Freddy Offenga]

Sergio wrote:
     Let me say some words about pure induction (dangerous) and "impro-
     ved" induction (better). The example below is from a novel of Sher-
     lock Holmes, as related by Kevin Korb in a paper (I can look up the
     reference if you want):
     ...
     where does the tentative explanatory hypotheses come from? In my
     vision, they *must* come from previous *inductive generalizations*,
     because any deductive form of reasoning cannot conclude nothing
     without correct antecedents. What Popperians seem to be using is
     another form of inductive reasoning, known as Abduction (detected by
     the first time by C. S. Peirce).

As I read in Haselager's book, the term 'abduction' indeed originates
from C. S. Peirce. The term (abduction) refers to the proces of genera-
ting hypotheses.
All those different terms confused me and now I see why. In one AI book
(Rich & Knight, 1991) I found the following description: "Given two wwf's
(A->B) and (B), for any expressions A and B, if it is consistent to
assume A, do so". Something similar can be found in Gerry's article 'Mul-
tiple alignment, cognition and computing'.
I'll mainly stick to Haselager's definitions. So far I've compiled the
following list:

- deductive reasoning (demonstrative)
     - monotonic
     - non-monotonic
- non-deductive reasoning (non-demonstrative)
     - enumerative induction
     - hypothetical induction (abduction)

I wrote here in my notes that the 'regularity' discussion is probably
about _making_ or _not making_ a distinction between the two mentioned
forms of induction. I'm not sure though.

Sergio:
     But this is not all. There's another detail that can improve induc-
     tive reasoning: it is what I call the "bayesian effect".
     ...
     What happened in our mind for us to gain such a certainty? 
     I believe that most of our daily decisions happen according to this
     process: we collect evidences and "conclude", by inductive generali-
     zation of several collaborative details, one thing or other. That
     does not mean we don't formulate explanations: even with plenty
     evidences we may be left with several "ambiguous" conditions. Then,
     it is time to devise experiments to check (a la Popper) which possi-
     ble explanation is the best. But the *root* of our reasoning chain
     appears to be inductive in essence.

Ok, I understand. This is called 'hypothetical induction' or 'inference
to the best explanation'. The following steps are distinguished:
(a) generating plausible hypothesis
(b) evaluation of hypothesis
An agent wondering what's going at a particular situation first performs
(a) and then (b). Now we can figure out how this is done by the SP
system. A related question: how does SP/CasC create a 'rule' by only
using these steps? This rule is valid because it holds important predic-
tions about the future.



Freddy Offenga

F.Offenga at student.kun.nl
Software Engineer and Student Cognitive Science at:
Katholieke Universiteit Nijmegen, The Netherlands