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Soundness and Completeness of a 4-Valued Bipolar Logic
Wen-Ran Zhang and Lulu Zhang

It is observed that bipolar equilibrium is natural reality or truth. Bipolarity, as an integral part of bipolar equilibrium, is inseparable from the truth. This paper first introduces a classification of unipolar and bipolar logical systems. Then, a 4-valued bipolar combinational logic BCL1 is introduced in the space B1 = {-1,0}x{0,1}. Soundness and completeness theorems are proved in a Hilbert style. It is shown that BCL1 is a generalization of Boolean logic and a non-linear fusion of two interactive Boolean subsystems, which is distinguished from linear logic, S5, bilattice, and intuitionistic fuzzy logic.

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