Abstract
To enhance the expressive power and the declarative ability of a deductive database, various CWA (Closed World Assumption) formalizations including the naive CWA, the generalized CWA and the careful CWA are extended to multi-valued logics. The basic idea is to embed logic formulas into some polynomial ring. The extensions can be applied in a uniform manner to any finitely multi-valued logics. Therefore they are also of computational significance.
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References
Bidoit N. Negation in rule-based database languages: A survey.Theoretical Computer Science, 1991, 78: 3–83.
Chazarain J, Riscos A, Alonso J A, Briales E. Multi-valued logic and Gröbner bases with applications to modal logic.J. Symbolic Computation, 1991, 11: 181–194.
Shepherdson J C. Negation as failure, completion and stratification. InHandbook of Logic in Artificial Intelligence and Logic Programming, Gabbay Dov Met al. (eds.), 1998, 5: 356–419.
Bolc L, Borowik P. Many-Valued Logics (1 Theoretical Foundations). Berlin Heidelberg: Springer-Verlag, 1992.
Cox D, Little J, O’Shea D. Ideals, Varieties, and Algorithms, — An Introduction to Computational Algebraic Geometry and Commutative Algebra. New York: Springer-Verlag, 1997.
Wu W-T. Basic Principles of Mechanical Theorem Proving in Geometries. Beijing: Science Press, 1984. (in Chinese).
Wu J, Tan H. An algebraic method to decide the deduction problem in many-valued logics. InProc. International Symposium on Multi-Valued Logics, IEEE Computer Society Press, 1994, pp.272–275.
Baaz M, Fermüller C G. Resolution-based theorem proving for many-valued logics.J. Symbolic Computation, 1995, 19: 353–391.
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On leave from School of Mathematical Sciences, Peking University.
WU Jinzhao was born in 1965. He obtained his Ph.D. degree in 1994 from the Institute of Systems Science, The Chinese Academy of Sciences. From 1994 to 1999 he was a postdoctor and research scientist in Peking University and Texas A&M University and Max-Planck Institute of Computer Science. Since 2000 he has been working on the Faculty of Mathematics and Computer Science, University of Mannheims.
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Wu, J. CWA formalizations in multi-valued logics. J. Comput. Sci. & Technol. 16, 263–269 (2001). https://doi.org/10.1007/BF02943204
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DOI: https://doi.org/10.1007/BF02943204