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European Conference on Multi-Agent Systems

International Conference on Agreement Technologies

EUMAS 2017, AT 2017: Multi-Agent Systems and Agreement Technologies pp 147–162Cite as

Decidable Term-Modal Logics

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10767))

Abstract

The paper considers term-modal logics and introduces some decidable fragments thereof. In particular, two fragments will be introduced: one that simulates monotone non-normal logics and another one that simulates normal multi-agent epistemic logics with quantification over groups of agents. These logics are defined semantically. Then, each of them is proof-theoretically characterized by a labelled calculus with good structural properties. Finally, we prove that each fragment considered is decidable, and we characterize the complexity of the validity problem for some of them.

Thanks are due to three anonymous referees and to the audience at EUMAS 2017, especially to Valentin Goranko, for helpful comments.

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Notes

  1. 1.

    See [19] for a term-modal like extension of the logic of belief KD45; and see [5,6,7] for extensions of TMLs, called indexed epistemic logics, with non-rigid designators.

  2. 2.

    See [24] for another way of expressing the minimal monotone logic M via TMLs.

References

  1. Ågotnes, T., Alechina, N.: Epistemic coalition logic: completeness and complexity. In: Proceedings of AAMAS 2012, 1099–1106 (2012)

    Google Scholar 

  2. Belardinelli, F., Lomuscio, A.: Quantified epistemic logic for reasoning about knowledge in multi-agent systems. Artif. Intell. 173, 982–1013 (2009)

    Article  MathSciNet  Google Scholar 

  3. Braüner, T., Ghilardi, S.: First-order modal logic. In: Blackburn, P., et al. (eds.) Handbook of Modal Logic, pp. 549–620. Elsevier, Amsterdam (2007)

    Google Scholar 

  4. Calardo, E., Rotolo, A.: Variants of multi-relational semantics for propositional non-normal modal logics. J. Appl. Non-Class. Log. 24, 293–320 (2014)

    Article  MathSciNet  Google Scholar 

  5. Corsi, G., Orlandelli, E.: Free quantified epistemic logics. Stud. Log. 101, 1159–1183 (2013)

    Article  MathSciNet  Google Scholar 

  6. Corsi, G., Orlandelli, E.: Sequent calculi for free quantified epistemic logics. In: Proceedings of ARQNL 2016, pp. 21–35. CEUR-WS (2016)

    Google Scholar 

  7. Corsi, G., Tassi, G.: A new approach to epistemic logic. In: Weber, E. (ed.) Logic, Reasoning, and Rationality, pp. 27–44. Springer, Dordrecht (2014). https://doi.org/10.1007/978-94-017-9011-6_2

    Chapter  Google Scholar 

  8. Dyckhoff, R., Negri, S.: Geometrization of first-order logic. Bull. Symb. Log. 21, 126–163 (2015)

    Article  Google Scholar 

  9. Fagin, R., et al.: Reasoning about Knowledge. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  10. Fitting, M., et al.: Term-modal logics. Stud. Log. 69, 133–169 (2001)

    Article  MathSciNet  Google Scholar 

  11. French, T., et al.: Succinctness of epistemic languages. In: Proceedings of IJCAI 2011, pp. 881–886. AAAI Press (2011)

    Google Scholar 

  12. Garg, D., et al.: Countermodels from sequent calculi in multi-modal logics. In: Proceedings of LICS 2012, pp. 315–324. IEEE Press (2012)

    Google Scholar 

  13. Gasquet, O., Herzig, A.: From classical to normal modal logics. In: Wansing, H. (ed.) Proof Theory of Modal Logic, pp. 293–311. Kluwer, Dordrecht (1996). https://doi.org/10.1007/978-94-017-2798-3_15

    Chapter  MATH  Google Scholar 

  14. Gilbert, D., Maffezioli, P.: Modular sequent calculi for classical modal logics. Stud. Log. 103, 175–217 (2015)

    Article  MathSciNet  Google Scholar 

  15. Grove, A., Halpern, J.: Naming and identity in epistemic logics part 1: the propositional case. J. Log. Comp. 3, 345–378 (1993)

    Article  Google Scholar 

  16. Halpern, J., Moses, Y.: A guide to completeness and complexity for modal logics of knowledge and belief. Artif. Intell. 54, 319–379 (1992)

    Article  MathSciNet  Google Scholar 

  17. Hansen, H.: Monotone Modal Logic (M.Th.). ILLC Preprints, Amsterdam (2003)

    Google Scholar 

  18. Kracht, M., Wolter, F.: Normal monomodal logics can simulate all others. J. Symb. Log. 64, 99–138 (1999)

    Article  MathSciNet  Google Scholar 

  19. Lomuscio, A., Colombetti, M.: QLB: a quantified logic for belief. In: Müller, J.P., Wooldridge, M.J., Jennings, N.R. (eds.) ATAL 1996. LNCS, vol. 1193, pp. 71–85. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0013578

    Chapter  Google Scholar 

  20. Negri, S., von Plato, J.: Proof Analysis. CUP, Cambridge (2011)

    Book  Google Scholar 

  21. Padmanabha, A., Ramanujam, R.: The monodic fragment of propositional term modal logic. Stud. Log. 1–25 (2018). Online First

    Google Scholar 

  22. Parikh, R.: The logic of games and its applications. In: Karpinski, M., van Leeuwen, J. (eds.) Topics in the Theory of Computation, pp. 119–139. Elsevier, Amsterdam (1985)

    Google Scholar 

  23. Pauly, M.: A modal logic for coalitional power in games. J. Log. Comput. 12, 149–166 (2002)

    Article  MathSciNet  Google Scholar 

  24. Sedlar, I.: Term-modal logic of evidence (2016). Unpublished paper

    Google Scholar 

  25. Vardi, M.: On the complexity of epistemic reasoning. In: Proceedings of LICS 1989, pp. 243–252. IEEE Press (1989)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Philosophy and Communication Studies, University of Bologna, Via Zamboni 38, 40126, Bologna, Italy

    Eugenio Orlandelli & Giovanna Corsi

Authors
  1. Eugenio Orlandelli
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  2. Giovanna Corsi
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Correspondence to Eugenio Orlandelli .

Editor information

Editors and Affiliations

  1. University of Évry Val d'Essonne, Paris Saclay, France

    Francesco Belardinelli

  2. Polytechnic University of Valencia, Valencia, Spain

    Estefanía Argente

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Orlandelli, E., Corsi, G. (2018). Decidable Term-Modal Logics. In: Belardinelli, F., Argente, E. (eds) Multi-Agent Systems and Agreement Technologies. EUMAS AT 2017 2017. Lecture Notes in Computer Science(), vol 10767. Springer, Cham. https://doi.org/10.1007/978-3-030-01713-2_11

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  • DOI: https://doi.org/10.1007/978-3-030-01713-2_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-01712-5

  • Online ISBN: 978-3-030-01713-2

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