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Non-triviality Done Proof-Theoretically

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10455)

Abstract

It is well known that naive theories of truth based on the three-valued schemes K3 and LP are non-trivial.

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Notes

  1. 1.

    See Gupta (1982), Kremer (1988), or Ripley (2012).

  2. 2.

    These two rules are based on those from Kremer (1988) and from Negri and von Plato (2001).

  3. 3.

    The appropriate [Cl] axiom for LP would be .

  4. 4.

    This problem was pointed out by Kremer (1988).

  5. 5.

    Negri and von Plato (2001, 32).

  6. 6.

    Note that we are assuming there are no function symbols in the language.

  7. 7.

    See Bimbó (2015, 36-51) for details.

  8. 8.

    Syntax consistency says, roughly, that the set of equalities on the left and negations of equalities on the right can be extended to an annotation set.

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Acknowledgments

We would like to thank the members of audiences at the Otago Logic Seminar and the Australasian Association for Logic Conference 2016 for feedback on this material. Shawn Standefer’s research was supported by the Australian Research Council, Discovery Grant DP150103801.

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Correspondence to Shawn Standefer .

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French, R., Standefer, S. (2017). Non-triviality Done Proof-Theoretically. In: Baltag, A., Seligman, J., Yamada, T. (eds) Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science(), vol 10455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55665-8_30

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  • DOI: https://doi.org/10.1007/978-3-662-55665-8_30

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