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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 8 (view source)
Revision as of 17:54, 20 August 2011
, 17:54, 20 August 2011→8.3.1. “Index” : A Program for Learning Formal Languages: + text
====8.3.1. “Index” : A Program for Learning Formal Languages====
====8.3.1. “Index” : A Program for Learning Formal Languages====
The program "Index" actualizes an inquiry driven system that learns formal languages, operating under a restricted notion of learning that is explained next.
To specify an inquiry driven system I can first describe it in static terms as a sign relation, and then elaborate the more dynamic aspects of its sign process. In this example the role of the object is played by a special kind of mathematical object, a formal system known as a "two level formal language".
The object o is a two level formal language over a finite alphabet A. The object domain O is the set of all such languages over the same alphabet.
A two level formal languge o is specified by giving its words and its phrases, o = <W, P> = <o.lex, o.lit>, two sets that comprise its "lexical" and "literal" levels, respectively.
The words of o are finite sequences of letters from the alphabet A, collectively forming a set W called the "lexicon" of o. In symbols, W(o) = o.lex c A*.
The phrases of o are finite sequences of words from the lexicon W, collectively forming a set P called the "liturgy" of o. In symbols, P(o) = o.lit c W*.
As mathematical objects, not to mention objects that are potentially infinite in their extension and presumably unknown to the agent at the beginning of inquiry, o and O have the status of "external objects". This means they do not inhabit the minds or computers, the original or extended media, of inquiry agents. External objects never have their being in the locus of representation but become known to the agent only by means of the signs that gradually come to inhere in its being.
Because the agent of inquiry has a limited capacity for taking up information, the process of becoming informed about an external object cannot be any form of direct instruction on the part of the object or perfect intuition on the part of the agent. It is always a matter of stepwise approximation to better representations of the object. The progress of inquiry accumulates the tokens of the object's features that successively impress themselves on the agent's medium of attention and integrates them into the ongoing process that constitutes a particular agent's total activity.
====8.3.2. “Study” : A Program for Reasoning with Propositions====
====8.3.2. “Study” : A Program for Reasoning with Propositions====