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Łukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems

Baianu, Professor I.C. and Georgescu, Professor George and Glazebrook, Professor James F. (2010) Łukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems. [Journal (Paginated)]

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Abstract

A novel approach to self-organizing, highly-complex systems (HCS), such as living organisms and artificial intelligent systems (AIs), is presented which is relevant to Cognition, Medical Bioinformatics and Computational Neuroscience. Quantum Automata (QAs) were defined in our previous work as generalized, probabilistic automata with quantum state spaces (Baianu, 1971). Their next-state functions operate through transitions between quantum states defined by the quantum equations of motion in the Schroedinger representation, with both initial and boundary conditions in space-time. Such quantum automata operate with a quantum logic, or Q-logic, significantly different from either Boolean or Łukasiewicz many-valued logic. A new theorem is proposed which states that the category of quantum automata and automata--homomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines) are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R)--Systems which are open, dynamic biosystem networks with defined biological relations that represent physiological functions of primordial organisms, single cells and higher organisms.

Item Type:Journal (Paginated)
Additional Information:http://www.edusoft.ro/brain/index.php/brain/article/view/97/201 ISSN: 2067-3957
Keywords:LM--algebraic logic, LM--logic algebras, algebraic category of LM-logic algebras, fundamental theorems of LM-logic algebra, non-linear genetic networks, nonlinear dynamics, Epigenomics, Cellular Interactomics, Immunology and hormonal regulatory systems, category theory, functors and natural transformations, toposes and Heyting logic algebras, quantum automata categories, limits and colimits, quantum automata homomorphisms, Abelian category, bicomplete categories, Quantum Relational Biology, generalised metabolic-replication, (M,R)--systems, complex bionetworks, quantum logic, non-commutative lattices, Hilbert space, quantum computers, computability of complex biological systems, Cartesian closed categories, extended quantum topos, category of groupoids, dynamic realisations of generalised (M,R)-systems (GMRs), category of GMRs, compact subsystems of GMR
Subjects:Biology > Theoretical Biology
Neuroscience > Computational Neuroscience
Computer Science > Complexity Theory
Computer Science > Dynamical Systems
Computer Science > Neural Nets
Neuroscience > Neurogenetics
Neuroscience > Neural Modelling
Neuroscience > Neurophysiology
ID Code:7751
Deposited By: Baianu, Professor I. C.
Deposited On:16 Dec 2011 00:58
Last Modified:16 Dec 2011 00:58

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References in Article

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