The structure of continuous logical functions

A method is described for structural analysis of continuous logical functions, CLFs, by using the theory of distributive grids. All CLFs which cannot be expanded into a sum are found. The existence and uniqueness of canonical CLF expansion is proved. Ranking relations are used in determining simple implicants. The necessary and sufficient conditions are determined under which a consistent phrase is a simple implicative CLF, The minimal disjunctive normal form is found to be univalent for a certain CLF range. Consensus is shown to be a sound technique in finding simple implicants. In a general case the minimal disjunctive normal form of the CLF cannot be determined univalently.