Titlebook: New Computational Paradigms; First Conference on S. Barry Cooper,Benedikt Löwe,Leen Torenvliet Conference proceedings 2005 Springer-Verlag

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Symbol Grounding in Connectionist and Adaptive Agent Models, characterized by the hypothesis that symbols are directly grounded into the agents’ own categorical representations, whilst at the same time having syntactic relationships with other symbols. The mechanism of grounding transfer is also introduced. This is the process by which the grounding of basic

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A Logical Approach to Abstract Algebra,ot only elementary but also mathematically simpler. We present an example where the simplification was significant enough to suggest an improved version of a classical theorem. For this we use a general method to transform some logically complex first-order formulae in a geometrical form which may b

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Schnorr Dimension,) of randomness. In contrast to computable randomness and Schnorr randomness, the dimension concepts defined via computable martingales and Schnorr tests coincide. Furthermore, we give a machine characterization of Schnorr dimension, based on prefix free machines whose domain has computable measure.

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Computability in Computational Geometry,putability for real numbers and real functions. In object directed computability, a geometric object is computable if it is the effective limit of a sequence of finitary objects of the same type as the original object, thus allowing a quantitative measure for the approximation. The domain-theoretic

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