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Indian Conference on Logic and Its Applications

ICLA 2019: Logic and Its Applications pp 132–143Cite as

Sequent Calculi for Normal Update Logics

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11600))

Abstract

Normal update logic is the temporalization of normal conditional logic. Sequent calculi for the least normal update logic \(\mathbf {UCK}\) by Andreas Herzig (1998) and some of its extensions are developed. The subformula property of these sequent calculi is shown by Takano’s semantic method. Consequently we prove the finite model property and decidability of these sequent calculi.

K. Sano—Partially supported by JSPS KAKENHI Grant-in-Aid for Young Scientists (B) Grant Number 15K21025 and Grant-in-Aid for Scientific Research (B) Grant Number 17H02258, and JSPS Core-to-Core Program (A. Advanced Research Networks).

M. Ma—Supported by the key project of National Social Science Found of China (Grant no. 18ZDA033).

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References

  1. Alenda, R., Olivetti, N., Pozzato, G.L.: Nested sequent calculi for normal conditional logics. J. Logic Comput. 26(1), 7–50 (2013)

    Article  MathSciNet  Google Scholar 

  2. Burgess, J.P.: Basic tense logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, Reidel, Dordrecht, vol. II, pp. 89–133 (1984)

    Google Scholar 

  3. Chellas, B.F.: Basic conditional logic. J. Philosophcal Logic 4(2), 133–153 (1975)

    Article  MathSciNet  Google Scholar 

  4. Chellas, B.F.: Modal Logic. Cambridge University Press, Cambridge (1980)

    Book  Google Scholar 

  5. de Swart, H.C.: A Gentzen-or Beth-type system, a practical decision procedure and a constructive completeness proof for the counterfactual logics VC and VCS. J. Symbolic Logic 48(1), 1–20 (1983)

    Article  MathSciNet  Google Scholar 

  6. Gent, P.: A sequent- or tableau-style system for Lewis’s counterfactual logic. Notre Dame J. Formal Logic 33(3), 369–382 (1992)

    Article  MathSciNet  Google Scholar 

  7. Gentzen, G.: Untersuchungen über das logische Schließen, Mathematische Zeitschrift, 39(1), pp. 176–210 (1935)

    Google Scholar 

  8. Girlando, M., Lellmann, B., Olivetti, N., Pozzato, G.L.: Standard sequent calculi for Lewis’ logics of counterfactuals. In: Michael, L., Kakas, A. (eds.) JELIA 2016. LNCS (LNAI), vol. 10021, pp. 272–287. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-48758-8_18

    Chapter  MATH  Google Scholar 

  9. Herzig, A.: Logics for belief base updating. In: Dubois, D., Przde, H. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management System, vol. 3, pp. 189–231. Springer, Dordrecht (1998). https://doi.org/10.1007/978-94-011-5054-5_5

    Chapter  Google Scholar 

  10. Kowalski, T., Ono, H.: Analytic cut and interpolation for bi-intuisionistic logic. The Review of Symbolic Logic, 10(2), pp. 259–283 (2017)

    Article  MathSciNet  Google Scholar 

  11. Lellmann, B., Pattinson, D.: Sequent systems for Lewis’ conditional logics. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds.) JELIA 2012. LNCS (LNAI), vol. 7519, pp. 320–332. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33353-8_25

    Chapter  MATH  Google Scholar 

  12. Maruyama, A.: Towards combined system of modal logics - a syntactic and semantic study, Ph.D. thesis, School of Information Science, Japan Advanced Institute of Science and Technology (2003)

    Google Scholar 

  13. Maruyama, A., Tojo, S., Ono, H.: Decidability of temporal epistemic logics for multi-agent models. In: Proceedings of the ICLP’01 Workshop on Computational Logic in Multi-Agent Systems (CLIMA-01), pp. 31–40 (2001)

    Google Scholar 

  14. Negri, S., Sabrdolini, G.: Proof analysis for Lewis counterfactuals. Rev. Symbolic Logic 9(1), 44–75 (2016)

    Article  MathSciNet  Google Scholar 

  15. Negri, S., Von Plato, J.: Structural Proof Theory. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  16. Nishimura, H.: A study of some tense logics by Gentzen’s sequential method. Publ. Res. Inst. Math. Sci. 16, 343–353 (1980)

    Article  MathSciNet  Google Scholar 

  17. Ohnishi, M., Matsumoto, K.: Gentzen method in modal calculi II. Osaka J. Math. 11(2), 115–120 (1959)

    MathSciNet  MATH  Google Scholar 

  18. Ono, H.: Semantical approach to cut elimination and subformula property in modal logic. In: Yang, S.C.-M., Deng, D.-M., Lin, H. (eds.) Structural Analysis of Non-Classical Logics. LASLL, pp. 1–15. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-48357-2_1

    Chapter  Google Scholar 

  19. Pattinson, D., Schröder, L.: Generic modal cut elimination applied to conditional logic. Logical Methods Comput. Sci. 7(1:4), 1–28 (2011)

    MathSciNet  MATH  Google Scholar 

  20. Takano, M.: Subformula property as a substitute for cut-elimination in modal propositional logics. Math. Jpn. 37(6), 1129–1145 (1992)

    MathSciNet  MATH  Google Scholar 

  21. Takano, M.: A modified subformula property for the modal logics K5 and K5D. Bull. Sect. Logic 30(2), 115–122 (2001)

    MathSciNet  MATH  Google Scholar 

  22. Takano, M.: A semantical analysis of cut-free calculi for modal logics. Rep. Math. Logic 53, 43–65 (2018)

    Google Scholar 

  23. Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory, 2nd edn. Cambridge University Press, Cambridge (2000)

    Book  Google Scholar 

  24. Zach, R.: Non-analytic tableaux for Chellas’s conditional logic CK and Lewis’s logic of counterfactuals VC. Australas. J. Logic 15(3), 609–628 (2018)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Graduate School of Letters, Hokkaido University, Sapporo, Japan

    Katsuhiko Sano

  2. Institute of Logic and Cognition, Sun Yat-Sen University, Guangzhou, China

    Minghui Ma

Authors
  1. Katsuhiko Sano
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  2. Minghui Ma
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Correspondence to Katsuhiko Sano .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Indore, Madhya Pradesh, India

    Md. Aquil Khan

  2. Indian Institute of Technology Goa, Goa, India

    Amaldev Manuel

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Sano, K., Ma, M. (2019). Sequent Calculi for Normal Update Logics. In: Khan, M., Manuel, A. (eds) Logic and Its Applications. ICLA 2019. Lecture Notes in Computer Science(), vol 11600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58771-3_13

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  • DOI: https://doi.org/10.1007/978-3-662-58771-3_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-58770-6

  • Online ISBN: 978-3-662-58771-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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