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Theory-relational belief revision

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Abstract

The prominent formal framework for belief change established by Alchourrón, Gärdenfors and Makinson circumscribes the territory of all rational belief-revision policies, encoded in the so-called AGM revision functions. A type of well-behaved and highly-expressive AGM revision function, induced from fixed total preorders over possible worlds, is that of uniform-revision operators (abbrev. UR operators). In this article, we introduce, both axiomatically and semantically (in terms of all popular constructive models for belief revision), a new class of AGM revision functions that is a proper sub-class of the class of AGM revision functions, but strictly larger (thus, more expressive) than the class of UR operators; hence, our proposal generalizes uniform revision. We call the presented operators theory-relational revision operators (abbrev. TR operators), since each such operator is uniquely defined through a single binary relation over theories of the language, called strong theory-relation. The connection between the semantic constructions of TR and UR operators is investigated, whereas, it is shown how a generalization (weakening) of a strong theory-relation —which is also a single fixed binary relation over theories, called weak theory-relation— can induce any AGM revision function. This latter result immediately proves an upper bound for the total number of AGM revision functions.

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References

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

    Article  MathSciNet  Google Scholar 

  2. Aravanis, T.: On uniform belief revision. J. Log. Comput. 30, 1357–1376 (2020)

    Article  MathSciNet  Google Scholar 

  3. Aravanis, T., Peppas, P., Williams, M.A.: An investigation of parametrized difference revision operators. Ann. Math. Artif. Intell. 89, 7–28 (2021)

    Article  MathSciNet  Google Scholar 

  4. Areces, C., Becher, V.: Iterable AGM functions. In: Mary-Anne Williams and Hans Rott, editors, Frontiers in Belief Revision, vol. 22 of Applied Logic Series, pp. 165–196, Springer, Dordrecht (2001)

  5. Darwiche, A., Pearl, J.: On the logic of iterated belief revision. Artificial Intelligence 89, 1–29 (1997)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  7. Gärdenfors, P., Makinson, D.: Revisions of Knowledge Systems Using Epistemic Entrenchment. In: Proceedings of the 2Nd Conference on Theoretical Aspects of Reasoning About Knowledge (TARK 1988), pp. 83–95, Pacific Grove, California, Morgan Kaufmann (1988)

  8. Grove, A.: Two modellings for theory change. J. Philos. Log. 17(2), 157–170 (1988)

    Article  MathSciNet  Google Scholar 

  9. Heltweg, P.: Implementing a Structured Approach to Belief Revision by Deterministic Switching Between Total Preorders, Master Thesis. University of Hagen, Germany (2021)

  10. Katsuno, H., Mendelzon, A.: Propositional knowledge base revision and minimal change. Artif. Intell. 52(3), 263–294 (1991)

    Article  MathSciNet  Google Scholar 

  11. Lehmann, D.: Belief Revision, Revised. In: Proceedings of the 14Th International Joint Conference on Artificial Intelligence (IJCAI 1995), pp. 1534–1540, Montreal, Quebec, Morgan Kaufmann Publishers Inc (1995)

  12. Parikh, R.: Beliefs, belief revision, and splitting languages. In: Lawrence S. Moss, Jonathan Ginzburg, and Maarten de Rijke, editors, Logic, Language and Computation, vol. 2, pp. 266–278. CSLI Publications (1999)

  13. Peppas, P.: Belief revision. In: Frank van Harmelen, Vladimir Lifschitz, and Bruce Porter, editors, Handbook of Knowledge Representation, pp. 317–359. Elsevier Science (2008)

  14. Peppas, P.: A panorama of iterated revision. In: Sven O. Hansson, editor, David Makinson on Classical Methods for Non-Classical Problems, pp. 71–94. Springer Netherlands (2014)

  15. Peppas, P., Williams, M.A.: Constructive modellings for theory change. Notre Dame J. Form. Log. 36(1), 120–133 (1995)

    Article  Google Scholar 

  16. Peppas, P., Williams, M.A.: Kinetic consistency and relevance in belief revision. In: Proceedings of the 15th European Conference on Logics in Artificial Intelligence (JELIA 2016), pp. 401–414 Springer International Publishing (2016)

  17. Peppas, P., Williams, M.A., Chopra, S., Foo, N.: Relevance in belief revision. Artif. Intell. 229, 126–138 (December 2015)

    Article  MathSciNet  Google Scholar 

  18. Rott, H.: A nonmonotonic conditional logic for belief revision. Part 1: Semantics and logic of simple conditionals. In: André Fuhrmann and Michael Morreau, editors, The Logic of Theory Change, volume 465 of Lecture Notes in Artificial Intelligence, pp. 135–181. Springer Berlin Heidelberg (1991)

  19. Schlechta, K.: Coherent Systems. Elsevier, Amsterdam (2004)

    MATH  Google Scholar 

Download references

Acknowledgments

The authors are thankful to the anonymous reviewers for their valuable comments on this article.

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Authors and Affiliations

  1. Department of Mechanical Engineering, School of Engineering, University of the Peloponnese, Patras, 263 34, Greece

    Theofanis Aravanis

  2. Department of Electrical and Computer Engineering, School of Engineering, University of Patras, Patras, 265 00, Greece

    Pavlos Peppas

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  1. Theofanis Aravanis
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Correspondence to Theofanis Aravanis.

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Aravanis, T., Peppas, P. Theory-relational belief revision. Ann Math Artif Intell 90, 573–594 (2022). https://doi.org/10.1007/s10472-022-09794-2

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Mathematics Subject Classification 2010