Soundness and Completeness of a 4-Valued Bipolar Logic

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Journal of multiple-valued logic and soft computing, Vol: 9, Issue: 3

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Zhang, Wen-Ran; Zhang, Lulu
Bipolar equilibrium; 4-valued bipolar logic; Unipolar logical systems; Bipolar logical systems; Boolean logic; Computer Sciences; Academic Units, Engineering & Computing, Computer Science, Computer Science Faculty Publications
article description
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.