HIERARCHY OF ALGEBRAIC BAYESIAN NETWORK GLOBAL STRUCTURES AS A SYSTEM OF GRAPHS AND HYPERGRAPHS
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Algebraic Bayesian networks are logical and probabilistic graphical models which make it possible to perform logical and probabilistic inference for knowledge uncertainty formalized via scalar and interval truth values of propositional formulae. Global structures of algebraic Bayesian network are overviewed; their systematization based on hypergraph representation is proposed and functional hierarchy of global structures is revealed. The proposed systematization gives the possibility to apply graph and hypergraph theory methods for solving a number of problems in analysis of algebraic Bayesian network global structures, in particular — to propose and justify a criterion for identification of its primary structure acyclicity, — and also gives the theoretical basis for algorithms of specified networks automated learning.