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On the Sharpness and the Single-Conclusion Property of Basic Justification Models

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Logical Foundations of Computer Science (LFCS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10703))

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Abstract

Justification Awareness Models, JAMs, were proposed by S. Artemov as a tool for modelling epistemic scenarios like Russell’s Prime Minister example. It was demonstrated that the sharpness and the single-conclusion property of a model play essential role in the epistemic usage of JAMs. The problem to axiomatize these properties using the propositional justification language was left opened. We propose the solution and define a decidable justification logic \(\mathsf{J}_{\text{ref}}\) that is sound and complete with respect to the class of all sharp single-conclusion justification models.

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Notes

  1. 1.

    In [3] they were referred as JEMs, Justification Epistemic Models. Later the terminology was changed, see [4].

  2. 2.

    In [3] they were referred as injective justifications. In [4] the terminology was changed.

  3. 3.

    In [9, 10] these variables are called reference constructions. In the context of Single-Conclusion Logic of Proofs they represent syntactical operations that restore some parts of a formula given its proof. It will be seen that v corresponds to the proof goal operation that extracts a formula from its proof.

  4. 4.

    The general second-order unification problem is known to be undecidable [5, 6]. In our case it is decidable. The problem is more simple because there is no nested occurrences of the function variable v in the language.

  5. 5.

    \(\theta \) is an infinite substitution of the form (3). We store the finite part of it.

References

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Acknowledgements

I would like to thank Sergei Artemov who attracted my attention to the problem.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119992, Russia

    Vladimir N. Krupski

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  1. Vladimir N. Krupski
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Correspondence to Vladimir N. Krupski .

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Editors and Affiliations

  1. City University of New York, New York, New York, USA

    Sergei Artemov

  2. Cornell University, Ithaca, New York, USA

    Anil Nerode

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Krupski, V.N. (2018). On the Sharpness and the Single-Conclusion Property of Basic Justification Models. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2018. Lecture Notes in Computer Science(), vol 10703. Springer, Cham. https://doi.org/10.1007/978-3-319-72056-2_13

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  • DOI: https://doi.org/10.1007/978-3-319-72056-2_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72055-5

  • Online ISBN: 978-3-319-72056-2

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