Continuous-valued Logic Algebra Department of Computer Sciences
Several non-standard logics were proposed to satisfy the need of uncertainty reasoning in intelligent information processing. They have characters of mathematical dialectical logic. Some of them are continuous-valued logic. Logical algebra is the foundation for constructing mathematical dialectical logic, just as Boolean algebra plays an important role in standard logic. The continuous-valued logic needs as foundation its logical algebra. In this tutorial, complete continuous-valued logic algebra is proposed, and the definitions of seven kinds of integrity cluster of logical operation model that may exist in continuous-valued propositional logic are given. Continuous-valued propositional logical operator models can directly include and deal with four uncertainties (dialectical contradictions). They are the uncertainty of propositional true degree arising from true /false (dialectical) contradictions, the uncertainty of logical operator model arising from enemy / friends (dialectical) contradictions, the uncertainty of logical operator model arising from loose/strict (dialectical) contradictions, and the uncertainty of logical operator model arising from familiar/unfamiliar (dialectical) contradictions. Using continuous-valued logic algebra can improve all kinds of existing continuous-valued propositional logical system, which is the important basis for further establishment of continuous-valued of dialectical logic.
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Bibliography [1] Huacan He, Pengtao Jia, Yingcang Ma, Lirong Ai, The outline on Continuous-valued logic algebra. International Journal of Advanced Intelligence. Volume 4, Number 1, 2013. [2] Huacan He, Hua Wang, Yonghuai Liu, Principle of Universal Logics, Beijing Sciene Press, Xi'an: NWPU Press, 2006. [3] Huacan He, Zhitao He, Yingcang Ma, Lirong Ai, Philosophical Significance of Universal Logic---On Second Revolution of Mathematical Logic in Perspectives on Universal Logic, Editors: Jean-Yves Beziau and Alexandre Costa-Leite, Polimetrica, Monza, 2007,. pp: 83-100 | ||||
