ONT Re: Inquiry Driven Systems
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Note 6
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Here is a Figure that serves to sum up the "analogy of experience".
o-----------------------------------------------------------o
| |
| K_pres |
| o |
| /|\ |
| / | \ |
| / | \ |
| / | \ |
| / Rule \ |
| / | \ |
| / | \ |
| / | \ |
| / E_poss \ |
| Fact / o \ Fact |
| / * * \ |
| / * * \ |
| / * * \ |
| / * * \ |
| / * * \ |
| / * Case Case * \ |
| / * * \ |
| / * * \ |
| /* *\ |
| o<<<---------------<<<---------------<<<o |
| E_past Analogy Morphism E_pres |
| More Known Less Known |
| |
o-----------------------------------------------------------o
Figure 1. Analogy of Experience
K_pres = Current knowledge base, say, in the form of a logical constraint.
It is convenient to have the option of expressing all logical statements
in terms of their models, that is, in terms of the primitive circumstances
or the elements of experience over which they hold true.
1. Let E_past be the chosen set of experiences,
or the circumstances that we have in mind
when we refer to "past experience".
2. Let E_poss be the collective set of experiences,
or the projective total of possible circumstances.
3. Let E_pres be the current experience, or the circumstances
that are present to the reasoner at the current moment.
If we think of the knowledge base K_pres as referring
to the "regime of experience" over which it is valid,
then all of these sets of models can be compared by the
simple relations of set inclusion or logical implication.
In these terms, the "analogy of experience" proceeds by inducing a Rule
about the validity of a current knowledge base and then deducing a Fact,
its applicability to a current experience, as in the following sequence:
Inductive Phase:
Given the Case: E_past => E_poss, Chosen events fairly sample Collective events.
Given the Fact: E_past => K_pres, Chosen events support the Knowledge regime.
Induce the Rule: E_poss => K_pres, Collective events support the Knowledge regime.
Deductive Phase:
Given the Case: E_pres => E_poss, Current events fairly sample Collective events.
Given the Rule: E_poss => K_pres, Collective events support the Knowledge regime.
Deduce the Fact: E_pres => K_pres, Current events support the Knowledge regime.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o