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An algebraic characterization of inductive soundness in proof by consistency

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Abstract

Kapur and Musser studied the theoretical basis for proof by consistency and obtained an inductive completeness result:p≡q if and only ifp=q is true in every inductive model. However, there is a loophole in their proof for the soundness part:p≡q impliesp=q is true in every inductive model. The aim of this paper is to give a correct characterization of inductive soundness from an algebraic view by introducing strong inductive models.

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References

  1. Kapur D, Musser D R. Proof by consistency.Artificial Intellgence, 1987, 31(2):125–157.

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  3. Burris S, Sankappanavar H P. A course in universal algebra. Springer-Verlag, New York, 1981.

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Authors and Affiliations

  1. Department of Computer Science, East China University of Science and Technology, 200237, Shanghai

    Shao Zhiqing & Song Guoxin

Authors
  1. Shao Zhiqing
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  2. Song Guoxin
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Additional information

This work was supported by the National Natural Science Foundation of China.

Shao Zhiqing received his B.S. degree in mathematical logic from nanjing University in 1986 and his M.S. degree in mathematical logic from the Chinese Academy of Sciences in 1989. He was a Assistant from 1989 to 1990 and has been a Lecturer since 1990 of the Department of Computer Science at the East China University of Science and Technology. Currently he is also a Ph.D. candidate in computer science at Shanghai Jiao Tong University. His research interests include logic, rewriting technique, parallel theory, and intelligent system.

Song Guoxin received his B.S. degree in architecture from Hehai University in 1968 and his M.S. degerr in computer software from Shanghai Jiao Tong University in 1983. Now he is a Professor and the Chairman of the Department of computer Science at the East China University of Science and Technology. His research interests include programming methodology, program verification, and concurrent engineering.

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Shao, Z., Song, G. An algebraic characterization of inductive soundness in proof by consistency. J. of Compt. Sci. & Technol. 10, 285–288 (1995). https://doi.org/10.1007/BF02943497

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  • DOI: https://doi.org/10.1007/BF02943497

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