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Sequent Systems for Nondeterministic Propositional Logics without Reflexivity

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Logic, Rationality, and Interaction (LORI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8196))

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Abstract

In order to deal with ambiguity in statements made in a natural language I introduce nondeterministic semantics for propositional logic with an arbitrary set C of connectives. The semantics are based on the idea that Γ entails \(\varDelta\) if and only if every possible deterministic disambiguation of Γ entails every possible deterministic disambiguation of \(\varDelta\). I also introduce a cut-free sequent style proof system S C that is sound and complete for the given semantics. Finally I show that while the semantics and proof system do not satisfy reflexivity they do allow certain kinds of substitution of equivalents.

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References

  1. Lewis, D.: Logic for equivocators. Noûs 16(3), 431–441 (1982)

    Article  Google Scholar 

  2. Avron, A., Lev, I.: Canonical propositional gentzen-type systems. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 529–544. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Avron, A., Lev, I.: Non-deterministic matrices. In: Proceedings of the 34th International Symposium on Multiple-Valued Logic, pp. 282–287 (2004)

    Google Scholar 

  4. Avron, A., Lev, I.: Non-deterministic multiple-valued structures. Journal of Logic and Computation 15(3), 241–261 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Barwise, J.: An introduction to first-order logic. In: Barwise, J. (ed.) Handbook of Mathematical Logic. Elsevier Science Publishers (1977)

    Google Scholar 

  6. Tychonoff, A.: Ein Fixpunktsatz. Mathematische Annalen 111(1), 767–776 (1935)

    Article  MathSciNet  Google Scholar 

  7. Tychonoff, A.: Über die topologische Erweiterung von Räumen. Mathematische Annalen 102(1), 544–561 (1930)

    Article  MathSciNet  Google Scholar 

  8. Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory. Cambridge University Press (1996)

    Google Scholar 

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

    Google Scholar 

  10. von Plato, J.: A proof of gentzen’s hauptsatz without multicut. Archive for Mathematical Logic 40(1), 9–18 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Groningen, The Netherlands

    Louwe B. Kuijer

Authors
  1. Louwe B. Kuijer
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Liverpool, Ashton Building, Ashton Street, L69 3BX, Liverpool, UK

    Davide Grossi

  2. Fakultät für Philosophie, Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, 80539, München, Germany

    Olivier Roy

  3. Center for the Study of Language and Cognition, Zhejiang University, Xixi Campus, Tianmushan Road 148, 310028,, Hangzhou, China

    Huaxin Huang

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Kuijer, L.B. (2013). Sequent Systems for Nondeterministic Propositional Logics without Reflexivity. In: Grossi, D., Roy, O., Huang, H. (eds) Logic, Rationality, and Interaction. LORI 2013. Lecture Notes in Computer Science, vol 8196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40948-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-40948-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40947-9

  • Online ISBN: 978-3-642-40948-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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