Decisions rules and flow networks

This paper, which is a continuation of a series of the author's papers on the relationship between decision algorithms and Bayes' theorem, is related to Łukasiewicz's ideas concerning the relationship between multivalued logic, probability and Bayes' theorem. We propose in this paper a new mathematical model of a flow network, different from that introduced by Ford and Fulkerson. Basically, the presented model is intended to be used rather as a mathematical model of decision processes than as a tool for flow optimization in networks. Moreover, it concerns rather flow of information than material media. Branches of the network are interpreted as decision rules with elementary conditions and decisions in the nodes, whereas the whole network represents a decision algorithm. It is shown that a flow in such networks is governed by Bayes' formula. In this case, however, the formula describes deterministic information flow distribution among branches of the network, without referring to its probabilistic character. This leads to a new look on Bayes' formula and many new applications.