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International Conference on Logic and Argumentation

CLAR 2020: Logic and Argumentation pp 80–95Cite as

Reasoning About Degrees of Confirmation

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12061))

Abstract

We present a probabilistic logic for reasoning about degrees of confirmation. We provide a sound and strongly complete axiomatization for the logic. We show that the problem of deciding satisfiability is in PSPACE.

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Notes

  1. 1.

    According to Eells and Fitelson [11].

  2. 2.

    The usual formulation of strong completeness is \(T\vdash \rho \) iff \(T\models \rho \). It is well known that this formulation is equivalent to the formulation of Theorem 4.

References

  1. Canny, J.F.: Some algebraic and geometric computations in PSPACE. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, Chicago, Illinois, USA, 2–4 May 1988, pp. 460–467 (1988)

    Google Scholar 

  2. Carnap, R.: Logical Foundations of Probability, 2nd edn. The University of Chicago Press, Chicago (1962). 1st edition (1950)

    MATH  Google Scholar 

  3. Delgrande, J.P., Renne, B., Sack, J.: The logic of qualitative probability. Artif. Intell. 275, 457–486 (2019)

    Article  MathSciNet  Google Scholar 

  4. Doder, D., Marinković, B., Maksimović, P., Perović, A.: A logic with conditional probability operators. Publications de L’Institut Mathematique Ns. 87(101), 85–96 (2010)

    Article  MathSciNet  Google Scholar 

  5. Doder, D., Ognjanović, Z.: A probabilistic logic for reasoning about uncertain temporal information. In: Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence, UAI 2015, pp. 248–257 (2015)

    Google Scholar 

  6. Doder, D., Ognjanović, Z.: Probabilistic logics with independence and confirmation. Studia Logica 105(5), 943–969 (2017)

    Article  MathSciNet  Google Scholar 

  7. Doder, D.: A logic with big-stepped probabilities that can model nonmonotonic reasoning of system P. Publications de L’Institut Mathematique Ns. 90(104), 13–22 (2011)

    Article  MathSciNet  Google Scholar 

  8. Doder, D., Marković, Z., Ognjanović, Z., Perović, A., Rašković, M.: A probabilistic temporal logic that can model reasoning about evidence. In: Link, S., Prade, H. (eds.) FoIKS 2010. LNCS, vol. 5956, pp. 9–24. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11829-6_4

    Chapter  Google Scholar 

  9. Doder, D., Ognjanovic, Z., Markovic, Z.: An axiomatization of a first-order branching time temporal logic. J. UCS 16(11), 1439–1451 (2010)

    MathSciNet  MATH  Google Scholar 

  10. Doder, D., Savić, N., Ognjanović, Z.: Multi-agent logics for reasoning about higher-order upper and lower probabilities. J. Logic Lang. Inf. 29, 77–107 (2020). https://doi.org/10.1007/s10849-019-09301-7

    Article  MathSciNet  Google Scholar 

  11. Eells, E., Fitelson, B.: Measuring confirmation and evidence. J. Philos. 97(12), 663–672 (2000)

    Article  MathSciNet  Google Scholar 

  12. Fagin, R., Halpern, J.Y.: Reasoning about knowledge and probability. J. ACM 41(2), 340–367 (1994)

    Article  MathSciNet  Google Scholar 

  13. Fagin, R., Halpern, J.Y., Megiddo, N.: A logic for reasoning about probabilities. Inf. Comput. 87, 78–128 (1990)

    Article  MathSciNet  Google Scholar 

  14. Fitelson, B.: The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philos. Sci. 66(3), 378 (1999)

    Article  MathSciNet  Google Scholar 

  15. Frisch, A., Haddawy, P.: Anytime deduction for probabilistic logic. Artif. Intell. 69, 93–122 (1994)

    Article  MathSciNet  Google Scholar 

  16. Gaifman, H.: A theory of higher order probabilities. In: Halpern, J.Y. (ed.) Proceedings of the Theoretical Aspects of Reasoning about Knowledge, pp. 275–292. Morgan-Kaufmann, San Mateo (1986)

    Chapter  Google Scholar 

  17. Guelev, D.: A propositional dynamic logic with qualitative probabilities. J. Philos. Logic 28, 575–605 (1999)

    Article  MathSciNet  Google Scholar 

  18. Halpern, J.Y.: An analysis of first-order logics of probability. Artif. Intell. 46, 311–350 (1990)

    Article  MathSciNet  Google Scholar 

  19. Heifetz, A., Mongin, P.: Probability logic for type spaces. Games Econ. Behav. 35, 31–53 (2001)

    Article  MathSciNet  Google Scholar 

  20. van der Hoek, W.: Some considerations on the logic P\(_{\rm {F}}\)D. J. Appl. Non-Class. Log. 7(3), 287–307 (1997)

    Google Scholar 

  21. Keisler, H.J.: Probability quantifiers. In: Barwise, J., Feferman, S. (eds.) Model Theoretic Logic, pp. 509–556. Springer, Berlin (1985)

    Google Scholar 

  22. Marinkovic, B., Ognjanovic, Z., Doder, D., Perovic, A.: A propositional linear time logic with time flow isomorphic to \(\omega \)\({}^{\text{2 }}\). J. Appl. Logic 12(2), 208–229 (2014)

    Article  MathSciNet  Google Scholar 

  23. Nilsson, N.: Probabilistic logic. Artif. Intell. 28, 71–87 (1986)

    Article  MathSciNet  Google Scholar 

  24. Ognjanović, Z., Rašković, M.: Some first-order probability logics. Theoret. Comput. Sci. 247(1–2), 191–212 (2000)

    Article  MathSciNet  Google Scholar 

  25. Ognjanović, Z., Rašković, M., Marković, Z.: Probability Logics. Probability-Based Formalization of Uncertain Reasoning. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-47012-2

    Chapter  MATH  Google Scholar 

  26. Ognjanović, Z., Doder, D., Marković, Z.: A branching time logic with two types of probability operators. In: Benferhat, S., Grant, J. (eds.) SUM 2011. LNCS (LNAI), vol. 6929, pp. 219–232. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23963-2_18

    Chapter  Google Scholar 

  27. Savić, N., Doder, D., Ognjanović, Z.: Logics with lower and upper probability operators. Int. J. Approximate Reasoning 88, 148–168 (2017)

    Article  MathSciNet  Google Scholar 

  28. Tentori, K., Crupi, V., Bonini, N., Osherson, D.: Comparison of confirmation measures. Cognition 103(1), 107–119 (2007)

    Article  Google Scholar 

  29. Tomović, S., Ognjanović, Z., Doder, D.: Probabilistic common knowledge among infinite number of agents. In: Destercke, S., Denoeux, T. (eds.) ECSQARU 2015. LNCS (LNAI), vol. 9161, pp. 496–505. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20807-7_45

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Matematički Institut SANU, Belgrade, Serbia

    Šejla Dautović & Zoran Ognjanović

  2. Utrecht University, Utrecht, The Netherlands

    Dragan Doder

Authors
  1. Šejla Dautović
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  2. Dragan Doder
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  3. Zoran Ognjanović
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Corresponding author

Correspondence to Dragan Doder .

Editor information

Editors and Affiliations

  1. Utrecht University, Utrecht, Utrecht, The Netherlands

    Mehdi Dastani

  2. Zhejiang University, Hangzhou, China

    Huimin Dong

  3. University of Luxembourg, Luxembourg, Luxembourg

    Leon van der Torre

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Dautović, Š., Doder, D., Ognjanović, Z. (2020). Reasoning About Degrees of Confirmation. In: Dastani, M., Dong, H., van der Torre, L. (eds) Logic and Argumentation. CLAR 2020. Lecture Notes in Computer Science(), vol 12061. Springer, Cham. https://doi.org/10.1007/978-3-030-44638-3_5

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  • DOI: https://doi.org/10.1007/978-3-030-44638-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-44637-6

  • Online ISBN: 978-3-030-44638-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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