🚀 go-pugleaf

Since this group seems dead, I am going to add my very meager voice to
the din to see if anybody is really out there --

If a >- h means "a is reason for concluding b"
and (a1 a2 a3 ... an) >- h means the same thing for the vector (a1 ...)
A defeasible rule is (a1 a2 a3 ... an) >- h, which for the limited
purposes of this post, I'll call X.  The "evidence" a0 a1 ... is 
the set of all observations within a well formed language, E.

Now, a rule has attributes, A(X).  For example, a rule that prohibits the
public display of campaign signs in residential areas might be described
as: (i) restricting the volume of political expression in residential areas,
(ii) making residential areas less "cluttered", or (iii) a property
use regulation.  The first attribute is descriptive/observed or computed. 
The second attributes attribute is a "purpose" for the rule. 
The third attribbute is more descriptive/categorical.  There are
obviously numerous attributes and even different type of attributes
for a given rule.  

We can also imagine "rules about rules" that involve reasoning about
rules using attributes.  If X* is the set of all rules, and A*(X*)
is the set of all attributes within the rule system X*, then a rule
about rules takes as antecedents some subset of A*(X*), and as a 
consequent some element of X* or its negation. E.g.,

	(b0 b1 b2 ... bn) >- G

where bi is an element of A*(X*), and G is an element of X*.

Okay.  Now, is A*(X*) a subset of E?  Similarly, is X* a subset of 
X? A superset?  Neither?

Note that in rule-formation, 
the rule maker often refers to hypothetical "results" of a rule under
consideration, and in articulating "purpose" also may refer to actual
"wrongs" that the rule is supposed to correct.  These are rationales for
a rule.  The question is whether reasoning with these rationales about
the rules themselves is any different than other reasoning, and how.

Just a thought.


 

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