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Truth and Preferences - A Game Approach for Qualitative Choice Logic

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Logics in Artificial Intelligence (JELIA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14281))

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Abstract

In this paper, we introduce game-theoretic semantics (GTS) for Qualitative Choice Logic (QCL), which, in order to express preferences, extends classical propositional logic with an additional connective called ordered disjunction. In particular, we present a new semantics that makes use of GTS negation and, by doing so, avoids contentious behavior of negation in existing QCL-semantics.

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Notes

  1. 1.

    Notice the flipped \(\ll \)-sign in the second case.

  2. 2.

    In the \(\textsf{coNP}\)-complete Unsat problem we are given a classical formula F and ask whether \(\mathcal {I} \not \models F\) for all interpretations \(\mathcal {I}\).

References

  1. Benferhat, S., Sedki, K.: Two alternatives for handling preferences in qualitative choice logic. Fuzzy Sets Syst. 159(15), 1889–1912 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. van Benthem, J.: Logic in Games. MIT Press, Cambridge (2014)

    Book  MATH  Google Scholar 

  3. Bernreiter, M., Lolic, A., Maly, J., Woltran, S.: Sequent calculi for choice logics. In: Blanchette, J., Kovács, L., Pattinson, D. (eds.) IJCAR 2022. LNCS, vol. 13385, pp. 331–349. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-10769-6_20

    Chapter  Google Scholar 

  4. Bernreiter, M., Maly, J., Woltran, S.: Choice logics and their computational properties. Artif. Intell. 311, 103755 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  5. Boudjelida, A., Benferhat, S.: Conjunctive choice logic. In: ISAIM 2016, Fort Lauderdale, Florida, USA, 4–6 January 2016 (2016)

    Google Scholar 

  6. Brewka, G., Benferhat, S., Berre, D.L.: Qualitative choice logic. Artif. Intell. 157(1–2), 203–237 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Charalambidis, A., Papadimitriou, G., Rondogiannis, P., Troumpoukis, A.: A many-valued logic for lexicographic preference representation. In: KR 2021, Online event, 3–12 November 2021, pp. 646–650 (2021)

    Google Scholar 

  8. Fermüller, C.G., Metcalfe, G.: Giles’s game and the proof theory of Łukasiewicz logic. Stud. Logica 92(1), 27–61 (2009)

    Article  MATH  Google Scholar 

  9. Freiman, R.: Games for hybrid logic. In: Silva, A., Wassermann, R., de Queiroz, R. (eds.) WoLLIC 2021. LNCS, vol. 13038, pp. 133–149. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-88853-4_9

    Chapter  MATH  Google Scholar 

  10. Hintikka, J.: Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic. Clarendon Press, Oxford (1973)

    MATH  Google Scholar 

  11. Hodges, W., Vänänen, J.: Logic and games. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, fall 2019 edn. (2019)

    Google Scholar 

  12. Pigozzi, G., Tsoukiàs, A., Viappiani, P.: Preferences in artificial intelligence. Ann. Math. Artif. Intell. 77(3–4), 361–401 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sedki, K., Lamy, J., Tsopra, R.: Qualitative choice logic for modeling experts recommendations of antibiotics. In: Proceedings of the Thirty-Fifth International Florida Artificial Intelligence Research Society Conference, FLAIRS 2022, Hutchinson Island, Jensen Beach, Florida, USA, 15–18 May 2022 (2022)

    Google Scholar 

  14. Tulenheimo, T.: Classical negation and game-theoretical semantics. Notre Dame J. Form. Logic 55(4), 469–498 (2014)

    MathSciNet  MATH  Google Scholar 

  15. Vänänen, J.: Models and Games. Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (2011)

    Google Scholar 

  16. Wagner, K.W.: Bounded query classes. SIAM J. Comput. 19(5), 833–846 (1990)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

We thank the anonymous reviewers for their feedback. This work was funded by the Austrian Science Fund (FWF) under grants P32830 and P32684, the Vienna Science and Technology Fund (WWTF) under grant ICT19-065, and partially funded by the EU (Marie Skłodowska-Curie RISE) project MOSAIC, grant 101007624.

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Authors and Affiliations

  1. Institute of Logic and Computation, TU Wien, Vienna, Austria

    Robert Freiman & Michael Bernreiter

Authors
  1. Robert Freiman
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  2. Michael Bernreiter
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Corresponding author

Correspondence to Robert Freiman .

Editor information

Editors and Affiliations

  1. TU Dresden, Dresden, Germany

    Sarah Gaggl

  2. Artificial Intelligence Research Institute - IIIA CSIC, Barcelona, Spain

    Maria Vanina Martinez

  3. Umeå University, Umeå, Sweden

    Magdalena Ortiz

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Freiman, R., Bernreiter, M. (2023). Truth and Preferences - A Game Approach for Qualitative Choice Logic. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_37

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  • DOI: https://doi.org/10.1007/978-3-031-43619-2_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43618-5

  • Online ISBN: 978-3-031-43619-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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