Bipolar logic and bipolar fuzzy logic - a unification of truth, fuzziness, and bipolarity

It is observed that bipolar equilibrium is truth. Bipolarity like fuzziness, as an integral part of truth, is inseparable from the truth. It is argued that Boolean logic and its extensions cannot be directly used to represent and reason with the coexistence of bipolar truth. A crisp bipolar combinational logic BCL_I and its fuzzy counterpart BCL_F are proposed for bipolar modeling based on the ancient Chinese Yin-Yang philosophy. The new family of logical systems is distinguished from other models. Bipolar zero-order completeness and 1st-order soundness are proved with a Hilbert style proof theory based on unipolar axioms and rules of inference. In addition, the lair´s case in the ancient paradox is redressed.