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Graded Consequence with Fuzzy Set of Premises

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Języki publikacji
EN
Abstrakty
EN
Fuzzy Logic a la Pavelka has been reintroduced here in terms of consequence relation instead of consequence operator. Metalogical notions like, consistency and inconsistency are proposed as graded notions. The relationship between consequence relation and inconsistency, both fuzzy here, is studied. Another metalogical notion viz., equivalence of two sets of formulae that originates from Tarski is defined and investigated in this context when the premise is a fuzzy set.
Wydawca
Rocznik
Strony
1--18
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
  • The Institute of Mathematical Sciences, Chennai, India
  • School of Cognitive Science, Jadavpur University Centre for Soft Computing and Research Indian Statistical Institute, Kolkata, India
Bibliografia
  • [1] M. K. Chakraborty. Use of fuzzy set theory in introducing graded consequence in multiple valued logic. In M.M. Gupta and T. Yamakawa, editors, Fuzzy Logic in Knowledge-Based Systems, Decision and Control, pages 247–257. Elsevier Science Publishers, B.V.(North Holland), 1988.
  • [2] M. K. Chakraborty. Graded consequence: further studies. Journal of Applied Non-Classical Logics, 5(2):127–137, 1995.
  • [3] M. K. Chakraborty and S. Basu. Graded consequence and somemetalogical notions generalized. Fundamenta Informaticae, 32:299–311, 1997.
  • [4] M. K. Chakraborty and S. Dutta. Graded consequence revisited. Mathware and Soft-Computing, accepted.
  • [5] M. K. Chakraborty and S. Dutta. Graded consequence revisited. Fuzzy Sets and Systems, 161(14):1885–1905, 2010.
  • [6] S. Dutta, S. Basu, and M.K. Chakraborty. Many-valued logics, fuzzy logics and graded consequence: a comparative appraisal. In K. Lodaya, editor, Proc. ICLA2013, LNCS 7750, pages 197–209. Springer, 2013.
  • [7] G. Gentzen. Investigations into logical deductions. In M.E. Szabo, editor, in the collected papers of G. Gentzen, pages 68–131. Elsevier Science Publishers, North Holland publication, Amsterdam, 1969.
  • [8] G. Gerla. Fuzzy Logic : Mathematical Tools for Approximate Reasoning. Kluwer Academic Publishers, Dordrecht, 2001.
  • [9] S. Gottwald. An approach to handle partially sound rules of inference. In B. Bouchon-Meunier, R. R. Yager, and L. A. Zadeh, editors, Advances in Intelligent Computing, IPMU’94, Selected papers, Lecture Notes Computer Sci. vol-945, pages 380–388. Elsevier Science Publishers, Springer: Berlin, 1995.
  • [10] P. Hájek. Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht, 1998.
  • [11] V. Novak. On syntactico-semantical completeness of first order fuzzy logic, parts i and ii. Kybernetica, 2, 6(1,2), Academia Praha:47–154, 1990.
  • [12] J. Pavelka. On fuzzy logic i, ii, iii. Zeitscher for Math. Logik und Grundlagen d. Math, 25:45–52, 119–134, 447–464, 1979.
  • [13] D.J. Shoesmith and T.J. Smiley. Multiple Conclusion Logic. Cambridge University Press, 1978.
  • [14] S.J. Surma. The growth of logic out of the foundational research in mathematics. In E. Agazzi, editor,Modern logic - a survey, pages 15–33. Elsevier Science Publishers, D. Reidel Publishing co., Dordrecht, 1981.
  • [15] A. Tarski. Methodology of deductive sciences. In Logic, Semantics, Metamathematics, pages 60–109. Elsevier Science Publishers, Clavendon Press, 1956.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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