Changes

=====4.3.4.2. Transfer=====

=====4.3.4.2. Transfer=====

What really gives a distinctively inductive character to the acquisition of a knowledge base is the "analogy of experience" that underlies its useful application.  Whenever we find ourselves prefacing an argument with the phrase, “If past experience is any guide … ” we can be sure this principle has come into play.  We are invoking an analogy between past experience, considered as a totality, and present experience, considered as a point of application.  What we mean in practice is this:  “If past experience is a fair sample of possible experience, then the knowledge gained in it applies to present experience.” This is the mechanism that allows a knowledge base to be carried across gulfs of experience that are indifferent to the effective contents of its rules.

What really gives a distinctively inductive character to the acquisition of a knowledge base is the "analogy of experience" that underlies its useful application.  Whenever we find ourselves prefacing an argument with the phrase "If past experience is any guide ... " we can be sure this principle has come into play.  We are invoking an analogy between past experience, considered as a totality, and present experience, considered as a point of application.  What we mean in practice is this:  "If past experience is a fair sample of possible experience, then the knowledge gained in it applies to present experience." This is the mechanism that allows a knowledge base to be carried across gulfs of experience that are indifferent to the effective contents of its rules.

Here are the details of how this works out in the "Rainy Day" example.  Let us consider a fragment K of the reasoner's knowledge base that is logically equivalent to the conjunction of two rules.

Here are the details of how this works out in the ''Rainy Day'' example.  Let us consider a fragment <math>K\!</math> of the reasoner's knowledge base that is logically equivalent to the conjunction of two rules.

K =  (B => A) and (B => D).

| <math>K \Leftrightarrow (B \Rightarrow A) \land (B \Rightarrow D).</math>

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.  Let C be a chosen set of experiences, or the circumstances we have in mind when we refer to "past experience".  Let C+ be a collective set of experiences, or the projective total of possible circumstances.  Let C be a current experience, or the circumstances present to the reasoner.  If we think of the knowledge base K as referring to the "regime of experience" over which it is valid, then all of these sets of models can be compared by simple relations of set inclusion or logical implication.

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.  Let <math>C^-\!</math> be a chosen set of experiences, or the circumstances we have in mind when we refer to "past experience".  Let <math>C^+\!</math> be a collective set of experiences, or the projective total of possible circumstances.  Let <math>C\!</math> be a current experience, or the circumstances present to the reasoner.  If we think of the knowledge base <math>K\!</math> as referring to the "regime of experience" over which it is valid, then all of these sets of models can be compared by 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 knowlege base and then deducing its applicability to a current experience.

In these terms, the "analogy of experience" proceeds by inducing a Rule about the validity of a current knowledge base and then deducing its applicability to a current experience.

C- => C+, "Chosen events fairly sample Collective events". (Case)

 

| width="20%" | <math>C^- \Rightarrow C^+,</math>

C- => K, "Chosen events support the Knowledge regime". (Fact)

| width="60%" | "Chosen events fairly sample Collective events".

 

| width="20%" | (Case)

C+ => K, "Collective events support the Knowledge regime". (Rule)

 

| <math>C^- \Rightarrow K,</math>

C => C+, "Current events fairly sample Collective events". (Case)

| "Chosen events support the Knowledge regime".

 

| (Fact)

C => K, "Current events support the Knowledge regime". (Fact)

| <math>C^+ \Rightarrow K,</math>

| "Collective events support the Knowledge regime".

| (Rule)

| <math>C \Rightarrow C^+,</math>

| "Current events fairly sample Collective events".

| (Case)

| <math>C \Rightarrow K,</math>

| "Collective events support the Knowledge regime".

| (Fact)

=====4.3.4.3. Testing=====

=====4.3.4.3. Testing=====