Metareasoning
Meta-reasoning Metareasoning
This topic has been under investigation by Don Perlis and his research group. Below is a paper that refers to past work. I have an interest in the concept as it relates to software engineering, as well as its implications for knowledge representation (see text below).


Authors: Mike Anderson, Don Perlis
Title: .pdf  Logic, self-awareness and self-improvement: The metacognitive loop and the problem of brittleness. Journal of Logic and Computation, 15(1):pp. 21-40, 2005.


Meta-reasoning refers to the process of taking reasoning off-line to decide what to reason about next. Typically, one thinks of a hierarchy of relationships in such reasoning, though this can lead one to a type of Zeno's paradox. To describe the nature of this paradox, one can first look at meta-mathematics. As defined, meta-mathematics contains all of the meaningful statements (e.g. in English, math symbols, instructions, and so forth) that are useful to guide a user's application of mathematics. Mathematics itself refers only to patterns of symbols, i.e. to the information that is separate from the verbal constructs associated with them. It is necessary to make this distinction, i.e. between mathematics and meta-mathematics because one construct merely provides the machinery (without an instruction manual) for the other to operate with.

However, there seems to be a limitless number of statements that can be said about mathematics, i.e. it appears that the information content associated with meta-mathematics is unbounded. This does not mean that meta-mathematics can not in some way, be 'quantified' (this in fact was done by Godel in his famous proof). It does, however point out the fact that meta-mathematics in and of itself isn't complete enough to describe all of the decisions or actions associated with mathematical expressions.

Q: Why isn't meta-mathematics enough?
A: The statements, though comprehensible to us, do not in themselves contain the necessary information on how to understand them, or for that matter, make the decisions on what to do with them.

Q: Then is there a meta-meta-mathematics and a meta-meta-meta-mathematics, etc....?
A: As finite beings operating with a finite amount of information we have to say no. Consider any other topic for example, such as playing chess. If each topic were to have its own exclusive meta~n-level, then, we would have a good deal of difficulty in applying them in practice. Consider, for example, the rigidity associated with object-oriented descriptions of objects. The descriptions are information-poor, so much so that to completely describe the possibilities associated with a particular concept or object, you might as well spend your time representing the states of all of the atoms on our planet.

Hence, there is a need to merge domains of knowledge, i.e. unify them together in a somewhat abstract fashion such that all concepts can stem from common, basic principles. This is how meta-reasoning should be formulated.

Q: How can a unified view of the world be created?
A: In one sense it can, in another it can't. It can't in the sense that knowledge really, in practice, is obtained through subjective experience. There doesn't appear to be a unique way to view any concept. However, there must be basic mechanisms by which new understanding, knowledge, etc. can be synthesized -- giving rise to a persistent 're-birth' process -- stitching together a seemingly complex representation of our understanding.