Given a static logical network, partition-based solutions are investigated. Easily verifiable necessary and sufficient conditions are obtained, and the corresponding formulas are presented to provide all types of the partition-based solutions. Then, the results are extended to mix-valued logical networks. Finally, two applications are presented: 1) an implicit function (IF) theorem of logical equations, which provides necessary and sufficient condition for the existence of IF and 2) converting the difference-algebraic network into a standard difference network.
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