Soundness and Completeness of a 4-Valued Bipolar Logic

Document Type


Publication Date


Publication Title

Journal of multiple-valued logic and soft computing


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 BCL 1 is introduced in the space B 1 = {-l,0}×{0,l}. Soundness and completeness theorems are proved in a Hilbert style. It is shown that BCL 1 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.