Complex non-linear biodynamics in categories, higher dimensional algebra and łukasiewicz–moisil topos: Transformations of neuronal, genetic and neoplastic networks [Book Review]

Axiomathes 16 (1-2):65-122 (2006)
Abstract
A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology.
Keywords adjoint functors and dynamically analogous systems  biogroupoids and organismal development  biological principles  nuclear equivalence and cell differentiation  categories   n-valued logics and higher dimensional algebra in neuroscience and genetics  cognitive and anticipatory processes  learning and quantum wave-pattern recognition  colimits  limits and adjointness relations in biology  generalized (M,R)-systems  neuro-categories and consciousness  quantum automata and relational biology  quantum bionetworks and their underlying quantum logics  quantum computers
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Rudolf Carnap (1937). The Logical Syntax of Language. London, K. Paul, Trench, Trubner & Co., Ltd..

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