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Article
Soundness and Completeness of a 4-Valued Bipolar Logic
Journal of multiple-valued logic and soft computing
  • Wen-Ran Zhang, Georgia Southern University
  • Lulu Zhang, University of Texas at Austin
Document Type
Article
Publication Date
1-1-2003
Disciplines
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.
Citation Information
Wen-Ran Zhang and Lulu Zhang. "Soundness and Completeness of a 4-Valued Bipolar Logic" Journal of multiple-valued logic and soft computing Vol. 9 Iss. 3 (2003)
Available at: http://works.bepress.com/wen-ran_zhang/35/