ÃLUKASIEWICZ-MOISIL MANY-VALUED LOGIC ALGEBRA OF HIGHLY-COMPLEX SYSTEMS

The fundamentals of ÃLukasiewicz-Moisil logic algebras and their applica-tions to complex genetic network dynamics and highly complex systems are presented in the context of a categorical ontology theory of levels, Medical Bioinformatics and self-organizing, highly complex systems. Quantum Au-tomata were defined in refs.[2] and [3] as generalized, probabilistic automata with quantum state spaces [1]. Their next-state functions operate through transitions between quantum states defined by the quantum equations of mo-tions in the Schrödinger representation, with both initial and boundary condi-tions in space-time. A new theorem is proven which states that the category of quantum automata and automata–homomorphisms has both limits and colim-its. Therefore, both categories of quantum automata and classical automata (sequential machines) are bicomplete. A second new theorem establishes tha