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A Consequence Relation for Graded Inference within the Frame of Infinite-valued Łukasiewicz Logic

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Języki publikacji
EN
Abstrakty
EN
We present a family of consequence relations for graded inference among Łukasiewicz sentences. Given a set of premises and a threshold η, we consider consequences those sentences entailed to hold to at least some degree ζ whenever the premises hold to a degree at least η. We focus on the study of some aspects and features of the consequence relations presented and, in particular, on the effect of variations in the thresholds η, ζ.
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77--95
Opis fizyczny
Bibliogr. 17 poz.
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autor
  • European Centre for Soft Computing Edificio Cientıfico Tecnológico, Gonzalo Guti´errez Quirós s/n 33600 Mieres, Spain
Bibliografia
  • [1] Bertsekas, D. Nonlinear Programming. Athena Scientific, 1999.
  • [2] Bou, F. A first approach to the deduction-detachment theorem in logics preserving degrees of truth. Proceedings of the 12th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, M´alaga, 2008. Magdalena, L., Ojeda-Aciego, M. and Verdegay, J. L. (eds.), 1061-1067.
  • [3] Bou, F. Infinite-valued Łukasiewicz logic based on principal lattice filters. Proceedings of the 40th International Symposium of Many Valued Logics, Barcelona, 2010. Esteva, F., Gispert, J. and Many´a, F. (eds.), 83-88.
  • [4] Boyd, S. and Vandenberghe, L. Convex Optimization. Cambridge University Press, 2004.
  • [5] Font, J.M., Gil, A.J., Torrens, A. and Verdu, V. On the infinite-valued Łukasiewicz logic that preserves degrees of truth. Archive for Mathematical Logic, 45/7 (2006), 839-868.
  • [6] Gerla, G. Fuzzy Logic: Mathematical Tools for Approximate Reasoning. Kluwer Academic Publishers, Dordrecht, 2001.
  • [7] Hájek, P. Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, 1998.
  • [8] Knight, K.M. Measuring inconsistency. Journal of Philosophical Logic, 31 (2002), 77-98.
  • [9] Marker, D. Model theory: An introduction. Graduate Texts in Mathematics, 217, Springer-Verlag, New York, 2002.
  • [10] McNaughton, R. A Theorem About Infinite-Valued Sentential Logic. The Journal of Symbolic Logic, Volume 16, Number 1 (1951), 1-13.
  • [11] Paris, J.B. The Uncertain Reasoner’s Companion. Cambridge University Press, 1994.
  • [12] Paris, J. B. Deriving information from inconsistent knowledge bases: A completeness theorem for n◃n Logic Journal of the IGPL, 12(5) (2004), 345-353.
  • [13] Paris, J. B., Picado Muiño, D. and Rosefield, M. Information from inconsistent knowledge: A probability logic approach. Interval / Probabilistic Uncertainty and Non-Classical Logics. Advances in Soft Computing, 46 (2008), 291-307.
  • [14] Paris, J. B., Picado Muiño, D. and Rosefield, M. Inconsistency as qualified truth: A probability logic approach. International Journal of Approximate Reasoning, 50 (2009), 1151-1163.
  • [15] Picado Muiño, D. Deriving information from inconsistent knowledge bases: A probabilistic approach. Ph.D Thesis. School of Mathematics. The University of Manchester, 2008.
  • [16] Picado Muiño, D. A graded inference approach based on infinite-valued Łukasiewicz semantics. Proceedings of the 40th International Symposium of Many Valued Logics, Barcelona, 2010. Esteva, F., Gispert, J. and Many´a, F. (eds.), 252-257.
  • [17] Picado Muiño, D. Measuring and repairing inconsistency in knowledge bases with graded truth. Fuzzy Sets and Systems (2011, to appear).
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-354538c6-5edd-4d98-9355-0676c8e74b35
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