A qualitative physics based on confluences
Artificial Intelligence - Special volume on qualitative reasoning about physical systems
Fuzzy Sets and Systems
Introduction to mathematical logic (3rd ed.)
Introduction to mathematical logic (3rd ed.)
Mind tools: the five levels of mathematical reality
Mind tools: the five levels of mathematical reality
Intrinsic mechanisms and application principles of general fuzzy logic through Yin-Yang analysis
Information Sciences—Informatics and Computer Science: An International Journal - Special issue using fuzzy algebraic structures in intelligent systems
Journal of the ACM (JACM)
An Investigation of the Laws of Thought
An Investigation of the Laws of Thought
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
YinYang bipolar dynamic logic (BDL) and equilibrium-based computational neuroscience
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
International Journal of Data Mining and Bioinformatics
A class of fuzzy multisets with a fixed number of memberships
Information Sciences: an International Journal
Bipolar queries: An aggregation operator focused perspective
Fuzzy Sets and Systems
Journal of Mathematical Imaging and Vision
Mathematical morphology on bipolar fuzzy sets: general algebraic framework
International Journal of Approximate Reasoning
Fuzzy Sets and Systems
Extended multi-polarity and multi-polar-valued fuzzy sets
Fuzzy Sets and Systems
Fuzzy logic and self-referential reasoning: a comparative study with some new concepts
Artificial Intelligence Review
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It is observed that equilibrium (including quasi- or non-equilibrium) is natural reality or bipolar truth. It is asserted that a multiple valued logic is a finite-valued extension of Boolean logic; a fuzzy logic is a real-valued extension of Boolean logic; Boolean logic and its extensions are unipolar systems that cannot be directly used to represent bipolar truth for visualization. To circumvent the representational limitations of unipolar systems, a zero-order (propositional) bipolar combinational logic BCL1 in the bipolar space B1={-1,0} × {0,1} is upgraded to a first-order (predicate) bipolar logic. BCL1 is then extended to an (n + 1)2-valued crisp bipolar combinational logic BCLn in the bipolar space Bn = {-n,...,-2,-1,0} × {0,1,2,...,n} and a real-valued bipolar fuzzy logic BCLF in the bipolar space BF = [-1,0] × [0,1]. A bipolar counterpart of unipolar axioms and rules of inference is introduced with the addition of bipolar augmentation. First-order consistency and completeness are proved. Depolarization functions are identified for the recovery of BCL1, BCLn, and BCLF to Boolean logic, a (n + 1)-valued logic, and fuzzy logic, respectively. Thus, BCL1, BCLn, and BCLF are bipolar generalizations or fusions of Boolean logic, multiple valued logic, and fuzzy logic, respectively. The bipolar family of systems provides a unique representation for bipolar knowledge fusion and visualization in an equilibrium world. The semantics of the bipolar systems are established, justified, and compared with unipolar systems. A redress is presented for the ancient paradox of the liar that leads to a few comments on Gödel's incompleteness theorem.