I tripped over my own boot-laces and stumbled – whacking my head. Bent over to rub my head and retie the damn laces, all a sudden I had the following quick rough thoughts for a paper:

'Cognitive Reflectivity' Marc Geddes Melbourne, Australia 18th June, 2009 Abstract "A change in the goal-system of an agent is equivalent to a change in the way in which knowledge is represented by the agent. It follows that it is equivalent to a change in the complexity of the program representing the agent. Thus we require a method of comparing the complexity of strings in order to ensure that relevant program structure is preserved with state transitions over time. Standard probability theory cannot be used because; (1) Consistent probability calculations require implicit universal generalizations, but a universal measure of the complexity of finite strings is a logical impossibility (fromGodel, Lob theorems); and (2) Standard measures of complexity (e.g Kolmogorov complexity) from information theory deal only with one aspect of information (i.e. Shannon information), and fail to consider semantic content. The solution must resolve both these problems. Regarding (2) the solution is as follows:, information theory is generalized to deal with the actual meaning of information (i.e . the semantics of Shannon information) .The generalized definition of the complexity of a finite string is based on the conceptual clustering of semantic categories specifying the knowledge a string represents. The generation of hierarchical category structures representing the knowledge in a string is also associated with a generalization of Occam’s razor. The justification for Occam’s razor and the problem of priors in induction is resolved by defining ‘utility’ in terms of ‘aesthetic goodness’, which is the degree of integration of different concept hierarchies. This considers the process through which a theory is generated; it is a form of process-oriented evaluation. Regarding (1); The Godel limitation is bypassed by using relative complexity measures of pairs of strings . This requires generalizing standard Bayesian induction ; in fact induction is merely a special case of a new form of case-based reasoning (analogical reasoning) . Analogical reasoning can be formalized by utilizing concepts from category theory to implement prototype theory, where mathematical categories are regarded as semantic categories. Semantic concepts representing the knowledge encoded in strings can be considered to reside in multi-dimensional feature space, and this enables mappings between concepts; such mappings are defined by functors representing conceptual distance; this gives a formal definition of an analogy. The reason this overcomes the Godel limitation and is more general than induction is because it always enables relative comparisons of the complexity of pairs of strings. This is because case-based reasoning depends only on the specific details on the strings being compared, whereas induction makes implicit universal generalizations, and thus fails. To summarize: Induction is shown to be merely a special case of a new type of generalized case-based (analogical) reasoning. Concepts from category theory enable a formal definition of an analogy, which is based on the notion of conceptual distance between concepts. The notion of complexity is generalized to deal with semantics, where the information in a string is considered to be a concept hierarchy. This enables comparisons between pairs of strings; relations between strings are defined in terms of the mappings between concepts, and the mapping is evaluated in terms of its aesthetic goodness. Godelian limitations are overcome, since analogical reasoning always enables a comparison of the relative complexity between any two finite strings. Further the new metric of aesthetic goodness ensures that the relevant program structure is preserved between state transitions and thus maintains a stable goal system." Cheers --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---