Soundness and Completeness of a 4-Valued Bipolar Logic

Document Type

Article

Publication Date

1-2003

Publication Title

Journal of Multiple-Valued Logic and Soft Computing

ISSN

1542-3980

Abstract

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.

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