Bipolar logic and bipolar knowledge fusion
Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997) - Tập 2 - Trang 1428-1433 vol.2
Tóm tắt
It is observed that Boolean logic is a unipolar logic defined in the unipolar space {0,1}. It is argued that a unipolar system cannot be directly used to represent and reason with the coexistence of bipolar truth. To circumvent the representational and reasoning limitations of unipolar systems, a 4-valued bipolar combinational logic BCL is introduced based on the ancient Chinese Yin-Yang philosophy. The new logic is defined in a strict bipolar space S = {- 1,0}/spl times/{0,1}, which is proved a generalization of Boolean logic and a fusion of two interactive unipolar subsystems. Bipolar tautologies including modus ponens are introduced for bipolar inference. The semantics of the new logic is established, justified, and compared with unipolar systems. Bipolar relations, bipolar transitivity, and polarized reflexivity are introduced. An O(n/sup 3/) algorithm is presented for bipolar transitive closure computation. In addition, the lair's case in the ancient paradox is redressed based on bipolar logic and bipolar relations.
Từ khóa
#Logic #Boolean functions #Polarization #Inference algorithms #Medical diagnostic imaging #Artificial intelligence #Knowledge representationTài liệu tham khảo
10.1117/12.460223
10.1016/j.ins.2003.05.010
10.1145/321105.321107
10.1109/21.24529
boole, 1854, An Investigation of the Laws of Thoughts
10.1007/978-94-010-1161-7_2
axelrod, 1976, Structure of Decision
lucker, 1987, Mind Tools - The Five Levels of Mathematical Reality
10.1093/logcom/1.1.41
10.1016/0004-3702(86)90090-1
10.1016/0004-3702(84)90037-7
bridge, 1977, Beginning Model Theory -The Completeness Theorem and Some Consequence
lukasiewicz, 1951, Aristotle's Syllogistic from the Standpoint of Modern Formal Logic
godel, 1930, Uber formal unentscheidbare satze der principia mathematica und verwandter systeme, Monatsh Math Phys, 37, 349