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Brazilian Conference on Intelligent Systems

BRACIS 2020: Intelligent Systems pp 272–287Cite as

Towards a Theory of Hyperintensional Belief Change

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12320))

Abstract

AGM’s belief revision is one of the main paradigms in the study of belief change operations. Despite its popularity and importance to the area, it is well recognized that AGM’s work relies on a strong idealisation of the agent’s capabilities and on the nature of beliefs themselves. Particularly, it is well-recognized in the area of Epistemology that Belief and Knowledge are hyperintensional notions, but to our knowledge only a few works have explicitly considered how hyperintensionality affects belief change. In this work, we investigate belief change operations based on Berto’s topic-sensitive framework and provide three different pseudo-contraction operations to account for the hyperintensional behaviour of beliefs. Our work highlights the connection of a foundational hyperintensional theory of belief with the results of AGM Belief Change. Also we propose and characterise different possible contraction-like operations in this framework.

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Notes

  1. 1.

    While AGM  [1] does not adhere to any specific logical language, the authors assume the logic is supraclassical, meaning it proves all truths of classical logic.

  2. 2.

    In the following, we will adopt Ribeiro and Wassermann’s  [29] generalisation of the AGM postulates, which correspond to a choice multiple contraction.

  3. 3.

    Namely, we can equivalently define \(\psi \in K-_{\downarrow \tau (\varphi )} \varphi \) by the formula \(B^{\psi \vee \lnot \psi }\psi \wedge B^{\lnot \varphi } \psi \) in their language.

  4. 4.

    Consider, for example, the case of searching for an algebraic proof for the Fundamental Theorem of Algebra. While we can prove this theorem by analytic methods, such a proof would not be desirable as it employs non-algebraic axioms and language.

  5. 5.

    Notice that the operations considered here are all defined as partial meet operations of some kind. As such, can can only guarantee the existence of such operations for foundational logics that are monotonic and compact, since otherwise the upper bound property [2] may not hold.

References

  1. Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symb. Logic 50(2), 510–530 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alchourrón, C.E., Makinson, D.: Hierarchies of regulations and their logic. In: Hilpinen, R. (ed.) New Studies in Deontic Logic. Studies in Epistemology, Logic, Methodology, and Philosophy of Science, vol. 152, pp. 125–148. Springer, Heidelberg (1981). https://doi.org/10.1007/978-94-009-8484-4_5

    Chapter  Google Scholar 

  3. Aucher, G.: When conditional logic and belief revision meet substructural logics. In: DARe-15 Defeasible and Ampliative Reasoning, Buenos Aires, Argentina (2015)

    Google Scholar 

  4. Badura, C., Berto, F.: Truth in fiction, impossible worlds, and belief revision. Aust. J. Philos. 97(1), 178–193 (2019)

    Article  Google Scholar 

  5. Berto, F.: Simple hyperintensional belief revision. Erkenntnis 84(3), 559–575 (2019). https://doi.org/10.1007/s10670-018-9971-1

    Article  MathSciNet  Google Scholar 

  6. Birkhoff, G.: Lattice Theory, vol. 25. American Mathematical Society, Providence (1940)

    MATH  Google Scholar 

  7. Bjerring, J.C.: Impossible worlds and logical omniscience: an impossibility result. Synthese 190(13), 2505–2524 (2013). https://doi.org/10.1007/s11229-011-0038-y

    Article  MATH  Google Scholar 

  8. Board, O.: Dynamic interactive epistemology. Games Econ. Behav. 49(1), 49–80 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cresswell, M.J.: Hyperintensional logic. Studia Logica: Int. J. Symb. Logic 34(1), 25–38 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cresswell, M.J., Von Stechow, A.: “de re” belief generalized. Linguist. Philos. 5, 503–535 (1982)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. Delgrande, J.P.: Horn clause belief change: contraction functions. In: KR, pp. 156–165 (2008)

    Google Scholar 

  13. Fermé, E., Wassermann, R.: On the logic of theory change: iteration of expansion. J. Braz. Comput. Soc. 24(1), 8 (2018). https://doi.org/10.1186/s13173-018-0072-4

    Article  Google Scholar 

  14. Flouris, G., Plexousakis, D., Antoniou, G.: On applying the AGM theory to DLs and OWL. In: Gil, Y., Motta, E., Benjamins, V.R., Musen, M.A. (eds.) ISWC 2005. LNCS, vol. 3729, pp. 216–231. Springer, Heidelberg (2005). https://doi.org/10.1007/11574620_18

    Chapter  Google Scholar 

  15. Gabbay, D., Rodrigues, O., Russo, A.: Belief revision in non-classical logics. Rev. Symb. Logic 1(03), 267–304 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gärdenfors, P.: Knowledge in Flux: Modeling the Dynamics of Epistemic States. The MIT Press, Cambridge (1988)

    MATH  Google Scholar 

  17. Girard, P., Rott, H.: Belief revision and dynamic logic. In: Baltag, A., Smets, S. (eds.) Johan van Benthem on Logic and Information Dynamics. OCL, vol. 5, pp. 203–233. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-06025-5_8

    Chapter  MATH  Google Scholar 

  18. Girard, P., Tanaka, K.: Paraconsistent dynamics. Synthese 193(1), 1–14 (2016). https://doi.org/10.1007/s11229-015-0740-2

    Article  MathSciNet  MATH  Google Scholar 

  19. Grove, A.: Two modelings for theory change. J. Philos. Logic 17(2), 157–170 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  20. Halpern, J.Y., Pucella, R.: Dealing with logical omniscience: expressiveness and pragmatics. Artif. Intell. 175(1), 220–235 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hansson, S.O.: Belief contraction without recovery. Studia Logica 50(2), 251–260 (1991). https://doi.org/10.1007/BF00370186

    Article  MathSciNet  MATH  Google Scholar 

  22. Hansson, S.O.: Defense of base contraction. Synthese 91(3), 239–245 (1992). https://doi.org/10.1007/BF00413568

    Article  MathSciNet  MATH  Google Scholar 

  23. Hansson, S.O., Wassermann, R.: Local change. Stud. Logica 70(1), 49–76 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  24. Jago, M.: Logical information and epistemic space. Synthese 167(2), 327–341 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Jin, Y., Thielscher, M.: Iterated belief revision, revised. Artif. Intell. 171(1), 1–18 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  26. Levesque, H.J.: A logic of implicit and explicit belief. In: Proceedings of the Fourth National Conference on Artificial Intelligence, pp. 198–202. American Association for Artificial Intelligence, Austin, August 1984

    Google Scholar 

  27. Rantala, V.: Impossible worlds semantics and logical omniscience. Acta Philosophica Fennica 35, 106–115 (1982)

    MathSciNet  MATH  Google Scholar 

  28. Ribeiro, J.S., Nayak, A., Wassermann, R.: Belief change and non-monotonic reasoning sans compactness. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, pp. 3019–3026 (2019)

    Google Scholar 

  29. Ribeiro, M.M., Wassermann, R.: Base revision for ontology debugging. J. Logic Comput. 19(5), 721–743 (2008). https://doi.org/10.1093/logcom/exn048. http://logcom.oxfordjournals.org/cgi/doi/10.1093/logcom/exn048

  30. Ribeiro, M.M., Wassermann, R., Flouris, G., Antoniou, G.: Minimal change: relevance and recovery revisited. Artif. Intell. 201, 59–80 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  31. Ribeiro, M.M.: Belief Revision in Non-classical Logics. Springer, Heidelberg (2012). https://doi.org/10.1007/978-1-4471-4186-0

    Book  MATH  Google Scholar 

  32. Rott, H.: Two dogmas of belief revision. J. Philos. 97(9), 503–522 (2000)

    Article  MathSciNet  Google Scholar 

  33. Rott, H., Pagnucco, M.: Severe withdrawal (and recovery). J. Philos. Logic 28(5), 501–547 (1999). https://doi.org/10.1023/A:1004344003217

    Article  MathSciNet  MATH  Google Scholar 

  34. Santos, Y.D., Matos, V.B., Ribeiro, M.M., Wassermann, R.: Partial meet pseudo-contractions. Int. J. Approx. Reason. 103, 11–27 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  35. Sedlár, I.: Hyperintensional logics for everyone. Synthese, pp. 1–24 (2019)

    Google Scholar 

  36. Souza, M., Moreira, Á., Vieira, R.: Dynamic preference logic as a logic of belief change. In: Madeira, A., Benevides, M. (eds.) DALI 2017. LNCS, vol. 10669, pp. 185–200. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-73579-5_12

    Chapter  MATH  Google Scholar 

  37. Van Benthem, J.: Dynamic logic for belief revision. J. Appl. Non-Class. Logics 17(2), 129–155 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  38. Wansing, H.: A general possible worlds framework for reasoning about knowledge and belief. Stud. Logica 49(4), 523–539 (1990). https://doi.org/10.1007/BF00370163

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Statistics, Federal University of Bahia - UFBA, Av. Adhemar de Barros, S/N, Ondina, Salvador, BA, Brazil

    Marlo Souza

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  1. Marlo Souza
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  1. Federal University of São Carlos, São Carlos, Brazil

    Ricardo Cerri

  2. Federal University of ABC, Santo Andre, Brazil

    Ronaldo C. Prati

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Souza, M. (2020). Towards a Theory of Hyperintensional Belief Change. In: Cerri, R., Prati, R.C. (eds) Intelligent Systems. BRACIS 2020. Lecture Notes in Computer Science(), vol 12320. Springer, Cham. https://doi.org/10.1007/978-3-030-61380-8_19

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  • DOI: https://doi.org/10.1007/978-3-030-61380-8_19

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