I've talked to a couple people since my last post, and I'm going to try another stab at laying out my current problem here.

I am primarily interested in refinement, by which I mean cognitive processes which modify successive iterations of an idea while seeking a solution which satisfies the semantics desired. In this context, refinement search is the process of seeking the next iteration during refinement. Additionally, for every iterative step, we will label the original item the parent, and the produced item the child.

The whole point of formal language design is to enable us to reliably produce languages in which refinement processes are well behaved: have minimal cost and introduce minimal distortions on the semantics of the system. We must therefore examine means of reducing the cost of refinement, and so we must examine the sources of these costs.

I conjecture that humans perform a good deal of their reasoning using their language centers, working with linguistic symbols; and that while meaningful statements in a given language are definitionaly backed by some deep structure meaning, in practice this deep structure is not constructed for most statements, and is certainly not constructed during refinement search. I will call this the search conjecture.

If the search conjecture is correct, then the cost of refinement search is a function of the cost of linguistic search, which proceeds by examining paradigmatic and syntactic variations on the parent statement, seeking a new statement which satisfies the desired semantics. This would introduce a local minimum problem, in that produced statements which are near enough to the semantics desired might be selected over other statements that were a better match, and thus semantically closer, if they entailed a shorter linguistic search to be reached.

A resulting normative rule for language design would be to attempt to structure language such that the average linguistic distance between two statements was proportional to their semantic distance (or the edit distance between their respective deep structures).

So my research needs to determine if the search conjecture can be backed up by existing theory and/or experimental results. If it can, then I need to work out a better means of presenting the consequences as a basis for normative linguistics.