Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

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

  • 62 Accesses

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.

This is a preview of subscription content, log in to check access.

References

  1. 1

    Popper K. The Logic of Scientific Discovery. New York: Routledge, 1959

  2. 2

    Popper K. Conjectures and Refutations. London: Routledge, 1963

  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. 35–132

  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: 510–530

  5. 5

    Bochman A. A foundational theory of belief and belief change. Artif Intell, 1999, 108: 309–352

  6. 6

    Fermé E, Hansson S O. AGM 25 years, twenty-five years of research in belief change. J Philos Logic, 2011, 40: 295–331

  7. 7

    Friedman N, Halpern J Y. Belief revision: a critique. J Logic Language Inf, 1999, 8: 401–420

  8. 8

    Darwiche A, Pearl J. On the logic of iterated belief revision. Artif Intell, 1997, 89: 1–29

  9. 9

    Li W. R-calculus: an inference system for belief revision. Comput J, 2007, 50: 378–390

  10. 10

    Friedberg R M. Two recursively enumerable sets of incomparable degrees of unsolvability. Proc Natl Acad Sci, 1957, 43: 236–238

  11. 11

    Muchnik A A. On the separability of recursively enumerable sets (in Russian). Dokl Akad Nauk SSSR, 1956, 109: 29–32

  12. 12

    Rogers H. Theory of Recursive Functions and Effective Computability. Cambridge: the MIT Press, 1987

  13. 13

    Soare R I. Recursively Enumerable Sets and Degrees, a Study of Computable Functions and Computably Generated Sets. Berlin: Springer-Verlag, 1987

  14. 14

    Takeuti G. Proof theory. In: Handbook of Mathematical Logic. Amsterdam: North-Holland. 1987

  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. 2329–2335

  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. 24–37

  17. 17

    Battiti R, Protasi M. Approximate algorithms and heuristics for MAXSAT. In: Handbook of Combinatorial Optimization. Boston: Springer, 1998. 77–148

  18. 18

    Hochbaum D S. Approximation Algorithms for NP-Hard Problems. Boston: PWS Publishing Company, 1997

  19. 19

    Katsuno H, Mendelzon A O. Propositional knowledge base revision and minimal change. Artif Intell, 1991, 52: 263–294

  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: 092101

Download references

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.

Author information

Correspondence to Yuefei Sui.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, W., Sui, Y. A computational framework for Karl Popper’s logic of scientific discovery. Sci. China Inf. Sci. 61, 042101 (2018). https://doi.org/10.1007/s11432-017-9199-8

Download citation

Keywords

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