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A computational framework for Karl Popper’s logic of scientific discovery

  • Wei Li
  • Yuefei Sui
Research Paper
  • 45 Downloads

Abstract

Belief revision is both a philosophical and logical problem. From Popper’s logic of scientific discovery, we know that revision is ubiquitous in physics and other sciences. The AGM postulates and R-calculus are approaches from logic, where the R-calculus is a Gentzen-type concrete belief revision operator. Because deduction is undecidable in first-order logic, we apply approximate deduction to derive an R-calculus that is computational and has finite injury. We further develop approximation algorithms for SAT problems to derive a feasible R-calculus based on the relation between deduction and satisfiability. In this manner, we provide a full spectrum of belief revision: from philosophical to feasible revision.

Keywords

belief revision logic of scientific discovery approximate deduction approximation algorithms feasible computation 

Notes

Acknowledgements

This work was supported by National Basic Research Program of China (973 Program) (Grant No. 2005CB321901), Open Fund of the State Key Laboratory of Software Development Environment (Grant No. SKLSDE-2010KF-06), and Beijing University of Aeronautics and Astronautics.

References

  1. 1.
    Popper K. The Logic of Scientific Discovery. New York: Routledge, 1959zbMATHGoogle Scholar
  2. 2.
    Popper K. Conjectures and Refutations. London: Routledge, 1963Google Scholar
  3. 3.
    Gärdenfors P, Rott H. Belief revision. In: Handbook of Logic in Artificial Intelligence and Logic Programming: Vol.4: Epistemic and Temporal Reasoning. Oxford: Oxford Science Publications, 1995. 35–132Google Scholar
  4. 4.
    Alchourrón C E, Gärdenfors P, Makinson D. On the logic of theory change: partial meet contraction and revision functions. J Symbo Logic, 1985, 50: 510–530MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bochman A. A foundational theory of belief and belief change. Artif Intell, 1999, 108: 309–352MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Fermé E, Hansson S O. AGM 25 years, twenty-five years of research in belief change. J Philos Logic, 2011, 40: 295–331MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Friedman N, Halpern J Y. Belief revision: a critique. J Logic Language Inf, 1999, 8: 401–420MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Darwiche A, Pearl J. On the logic of iterated belief revision. Artif Intell, 1997, 89: 1–29MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Li W. R-calculus: an inference system for belief revision. Comput J, 2007, 50: 378–390CrossRefGoogle Scholar
  10. 10.
    Friedberg R M. Two recursively enumerable sets of incomparable degrees of unsolvability. Proc Natl Acad Sci, 1957, 43: 236–238CrossRefzbMATHGoogle Scholar
  11. 11.
    Muchnik A A. On the separability of recursively enumerable sets (in Russian). Dokl Akad Nauk SSSR, 1956, 109: 29–32MathSciNetzbMATHGoogle Scholar
  12. 12.
    Rogers H. Theory of Recursive Functions and Effective Computability. Cambridge: the MIT Press, 1987zbMATHGoogle Scholar
  13. 13.
    Soare R I. Recursively Enumerable Sets and Degrees, a Study of Computable Functions and Computably Generated Sets. Berlin: Springer-Verlag, 1987zbMATHGoogle Scholar
  14. 14.
    Takeuti G. Proof theory. In: Handbook of Mathematical Logic. Amsterdam: North-Holland. 1987Google Scholar
  15. 15.
    Li W, Sui Y F. The R-calculus and the finite injury priority method. In: Proceedings of IEEE International Conference on Robotics & Automation, Singapore, 2017. 2329–2335Google Scholar
  16. 16.
    Asano T. Approximation algorithms for MAX SAT: Yannakakis vs. Goemans-Williamson. In: Proceedings of the 5th Israel Symposium on Theory of Computing and Systems, Ramat-Gan, 1997. 24–37Google Scholar
  17. 17.
    Battiti R, Protasi M. Approximate algorithms and heuristics for MAXSAT. In: Handbook of Combinatorial Optimization. Boston: Springer, 1998. 77–148CrossRefGoogle Scholar
  18. 18.
    Hochbaum D S. Approximation Algorithms for NP-Hard Problems. Boston: PWS Publishing Company, 1997zbMATHGoogle Scholar
  19. 19.
    Katsuno H, Mendelzon A O. Propositional knowledge base revision and minimal change. Artif Intell, 1991, 52: 263–294MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Li W, Sui Y F, Sun M Y. The sound and complete R-calculus for revising propositional theories. Sci China Inf Sci, 2015, 58: 092101MathSciNetGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Software Development EnvironmentBeihang UniversityBeijingChina
  2. 2.Key Laboratory of Intelligent Information Processing, Institute of Computing TechnologyChinese Academy of SciencesBeijingChina

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