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The Sequent Systems and Algebraic Semantics of Intuitionistic Tense Logics

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Logic, Rationality, and Interaction (LORI 2019)

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Abstract

In this paper we consider a weak Ewald’s intuitionistic tense logic (wIK.t). We study its sequent system and algebraic semantics. We prove the soundness and the completeness results. We also show that the sequent system for wIK.t introduced in the present paper admits cut elimination. Finally we propose a criterion and prove that all extensions of wIK.t satisfying this criterion have cut free sequent systems.

The work of both authors were supported by Key program of Chongqing’s Key Research Institute of Humanities and Social Sciences (No. 14SKB044).

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References

  1. Bull, R.A.: Some modal calculi based on IC. Stud. Logic Found. Math. 40, 3–7 (1965)

    Article  MathSciNet  Google Scholar 

  2. Burgess, J.P.: Basic Tense Logic. Springer, Dordrecht (1984)

    Book  Google Scholar 

  3. Buszkowski, W.: Interpolation and FEP for logics of residuated algebras. Logic J. IGPL 19(3), 437–454 (2018)

    Article  MathSciNet  Google Scholar 

  4. Chajda, I.: Algebraic axiomatization of tense intuitionistic logic. Cent. Eur. J. Math. 9(4), 1185–1191 (2011)

    Article  MathSciNet  Google Scholar 

  5. Ewald, W.: Intuitionistic tense and modal logic. J. Symb. Logic 51(1), 166–179 (1986)

    Article  MathSciNet  Google Scholar 

  6. Figallo, A., Pelaitay, G.: An algebraic axiomatization of the Ewald’s intuitionistic tense logic. Soft. Comput. 18(10), 1873–1883 (2014)

    Article  Google Scholar 

  7. Fitting, M.: Nested sequents for intuitionistic logics. Notre Dame J. Formal Logic 1(1), 41–61 (2014)

    Article  MathSciNet  Google Scholar 

  8. Galmiche, D., Yakoub, S.: Label-free natural deduction systems for intuitionistic and classical modal logics. J. Appl. Non-Class. Logics 20(4), 373–421 (2010)

    Article  MathSciNet  Google Scholar 

  9. Gore, R., Postniece, L., Tiu, A.: Cut-elimination and proof search for bi-intuitionistic tense logic. In: Valentin, S., Beklemishev, L., Valentin, G. (eds.) Advances in Modal Logic, pp. 156–177. College Publications, London (2010)

    MATH  Google Scholar 

  10. Simpson, A.K.: The proof theory and semantics of intuitionistic modal logic (1994)

    Google Scholar 

  11. Straßburger, L.: Cut elimination in nested sequents for intuitionistic modal logics. In: Pfenning, F. (ed.) FoSSaCS 2013. LNCS, vol. 7794, pp. 209–224. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-37075-5_14

    Chapter  Google Scholar 

  12. Versmissen, J.: Grammatical composition: modes, models, modalities: logical and linguistic aspects of multimodal categorial grammars (2001)

    Google Scholar 

  13. Zhe, L.: Non-associative Lambek calculus with modalities: interpolation, complexity and FEP. Logic J. IGPL 22(3), 494–512 (2014)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Philosophy, Peking University, Beijing, China

    Kaiyang Lin

  2. Institute of Logic and Intelligence, Southwest University, Chongqing, China

    Zhe Lin

  3. Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou, China

    Zhe Lin

Authors
  1. Kaiyang Lin
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  2. Zhe Lin
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Corresponding author

Correspondence to Zhe Lin .

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Editors and Affiliations

  1. Roskilde University, Roskilde, Denmark

    Patrick Blackburn

  2. Université Paul Sabatier, IRIT-CNRS, Toulouse, France

    Emiliano Lorini

  3. Southwest University, Chongqing, China

    Meiyun Guo

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Lin, K., Lin, Z. (2019). The Sequent Systems and Algebraic Semantics of Intuitionistic Tense Logics. In: Blackburn, P., Lorini, E., Guo, M. (eds) Logic, Rationality, and Interaction. LORI 2019. Lecture Notes in Computer Science(), vol 11813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60292-8_11

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  • DOI: https://doi.org/10.1007/978-3-662-60292-8_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-60291-1

  • Online ISBN: 978-3-662-60292-8

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