Bipolar logic and bipolar knowledge fusion

It is observed that Boolean logic is a unipolar logic defined in the unipolar space {0,1}. It is argued that a unipolar system cannot be directly used to represent and reason with the coexistence of bipolar truth. To circumvent the representational and reasoning limitations of unipolar systems, a 4-valued bipolar combinational logic BCL is introduced based on the ancient Chinese Yin-Yang philosophy. The new logic is defined in a strict bipolar space S = {-1,0} x {0,1}, which is proved a generalization of Boolean logic and a fusion of two interactive unipolar subsystems. Bipolar tautologies including modus ponens are introduced for bipolar inference. The semantics of the new logic is established, justified, and compared with unipolar systems. Bipolar relations, bipolar transitivity, and polarized reflexivity are introduced. An O(n(3)) algorithm is presented for bipolar transitive closure computation. In addition, the lair's case in the ancient paradox is redressed based on bipolar logic and bipolar relations.