The conceptual and technical basics for qualimetry of models and multiple–model complexes
Sokolov, Yusupov · Informatics and Automation · 2014
An ideal of conjunctions with a probabilistic estimates/assignment of its elements is one of the mathematical models of a knowledge pattern with probabilistic uncertainty. Chains and networks of such ideals are mathematical models of knowledge pattern bases; these models are referred to as algebraic Bayesian networks. We consider extremal tasks that appear in conjunction chains ideals when elementary evidence or a set of such evidence is propagated over them. This propagation is referred to as à posteriori inference. We also generalize our approach to evidence propagation onto chains of conjunctions ideals and acyclic networks of those ideals. Initially appearing extremal tasks are hyperbolic programming ones; but we manage to reduce them to linear programming tasks. We describe as well an indexation of ideal elements. This indexation allows to formally specify a set of constraints, originated from probabilistic logic axioms, over a conjunctions ideal. This formal specification allows a convenient notation of the extremal tasks under question.