Abstract
John McCarthy proposed non-monotonic reasoning for incomplete information in which reasoning is changed if knowledge is added to the system. Non-monotonic reasoning. Nonmonotonic Problems are undecided. An undecided problem has no solution. A method needed to solve undecided AI problems. In this paper, fuzzy modeling for non-monotonic logic is studied as method for non-monotonic reasoning. The Fuzzy non-monotonic reasoning is studied with a twofold fuzzy logic. Fuzzy truth maintenance system (FTMS) is studied for fuzzy non-monotonic reasoning. Fuzzy logic programming is given for non-monotonic reasoning some examples are discussed for fuzzy non-monotonic reasoning.

Keywords
fuzzy Sets, twofold fuzzy sets, non-monotonic reasoning, fuzzy non-monotonic reasoning, incomplete knowledge, FTMS, fuzzy logic programming

Cite this paper
Poli Venkata Subba Reddy, Fuzzy Non-monotonic Logic , SCIREA Journal of Computer. Volume 4, Issue 1, February 2019 | PP. 1-12.

References

[ 1 ]	A. Bochnan, A Logical Theory of Non-monotonoc Inference and Belief Change, Springer 2001.
[ 2 ]	Allen, J.F. Natural Language Understanding, Benjamin Cummings, 1987, Second Edition, 1994.
[ 3 ]	.J. Doyle, A Truth Maitance System, Artificial Intelligence, Vol.11, No.3, 1979.
[ 4 ]	Jhon McCarthy, Circumscription – A Form of Non-monotonic Reasoning, Artificial Intelligence, Vol.13, pp.27-39, 1980..
[ 5 ]	E. H. Mamdani, Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Synthesis, IEEE Transactions on Computers, vol.C-28,issue.2, pp.1182-1191, 1977.
[ 6 ]	N. Rescher, Many-Valued Logic, McGrow-Hill, New York, 1969.
[ 7 ]	Poli Venkata Subba Reddy, “Fuzzy Conditional Inference for Medical Diagnosis”, Second International Conference on Fuzzy Theory and Technology, Advancess in Fuzzzy Theory and Technology, Vol.2, University of North-Carolina, Duke University, November13-16, 1993, USAL.
[ 8 ]	Poli Venkata Subba reddy and M. Syam Babu, ‘Some Methods of Reasoning for Conditional Propositions”, Fuzzy Sets and Systems, vo.52,pp.229-250,1992.
[ 9 ]	Poli Venkata subba reddy, Fuzzy logic based on Belief and Disbelief membership functions, Fuzzy Information and Engineering, Volume 9, Issue 4, December 2017, Pages 405-422.
[ 10 ]	L.A. Zadeh, ”Calculus of Fuzzy restrictions”, Fuzzy sets and their applications to cognitive and decision processes, L.A.Zadeh,K.S.Fu,M.Shimura,Eds,New York, Academic, 1975, pp.1-39.
[ 11 ]	L.A Zadeh,” Fuzzy sets”, Information Control,.vol.8,3pp.38-353, 1965.
[ 12 ]	L.A Zadeh , A Note on Z-numbers, Fuzzy Information Science, vol.181, pp.2923-2932, 2011.
[ 13 ]	L.A Zadeh, fuzzy sets and Information Granularity, Selected Papers bt L.A. Zadeh,pp.432-448, 1979.
[ 14 ]	J. M. Won, S. Y. Park, and J. S. L ee, Parameter conditions for monotonic Takagi-Sugeno-Kang fuzzy system, Fuzzy Sets and Systems, vol.132, pp.135-146, 2002.
[ 15 ]	E. V. Broekhoven and B. D. Baets, Monotone Mamdani-Assilian models under mean of maxima defuzzification, Fuzzy Sets and Systems, vol. 159, pp.2819-2844, 2008.
[ 16 ]	E. V. Broekhoven and B. De Baets, Only smooth rule bases can generate monotone Mamdani-Assilian models under COG defuzzification,IEEE Trans. Fuzzy Systems, vol. 17, no. 5, pp. 1157-1174, 2009.
[ 17 ]	H.Seki, H. Ishii, and M. Mizumoto, On the monotonicity of fuzzy-inference methods related to T-S inference method, IEEE Trans. Fuzzy Systems, vol. 18, no. 3, pp. 629-634, 2010.