Dynamical duality of type- and token-computation as an abstract brain

In brain science, there are few researches focusing on the theoretical relation between cognition (top-down processing) and perception (bottom-up processing). Philosophically they were regarded as the alternative leading to the dualism of mind and body, while it is an adequate problem for the endo-physics. Qualia are conjectured as the hard problem under those situations. To overcome such an impasse, we propose an abstract brain model featuring the dynamical duality of two parts of computations in a brain, in a term of endo-physics and internal measurement. Two parts of computations are expressed as binary relations, and the relationship between them is expressed as a pair of maps, called an infomorphism [Barwise J, Seligman J. Information flow, the logic of distributed systems. Cambridge University Press 1997]. Dynamical duality is implemented by the interaction between a binary relation and an infomorphism, and that leads to a dynamical change of a pair of binary relations. When a binary relation is expressed as a partial ordered set, one can check whether a part of computation is closed with respect to logical operations (i.e., a lattice) or not. By estimating a binary relation in terms of properties of lattice, we show that dynamical infomorphism robustly develops to a pair of logical computations corresponding to type cognition and non-logical one corresponding to qualia perception. It implies origin of differentiation and robust co-existence of type-cognition and qualia-perception. It is easy to see that dynamical infomorphism can also develop to a pair of singleton sets corresponding to savants' special cognitive style