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International Workshop on Logic, Rationality and Interaction

LORI 2019: Logic, Rationality, and Interaction pp 286–296Cite as

Knowledge in Topological Argumentation Models

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11813))

Abstract

We formalise justification in the topological argumentation model and define knowledge and belief based on justification. In addition to revealing that the notions of knowledge and belief based on justification satisfy Stalnaker’s BK system except for the closure principle, the main contribution of this paper is a counter-intuitive result about the notion of knowledge based on justification, which is related to the no false lemmas.

The research in this paper is supported by the Major Program of the National Social Science Foundation of China (NO. 17ZDA026).

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Notes

  1. 1.

    When no confusion arises, \(\tau _{\mathcal {E}_0}\) will be denoted simply by \(\tau \).

  2. 2.

    A topology over a non-empty domain X is a family \(\tau \subseteq 2^X\) containing both X and \(\varnothing \), and closed under both finite intersections and arbitrary unions. The elements of a topology are called open sets. The topology generated by a given \(\mathcal {Y}\subseteq 2^X\) is the smallest topology \(\tau _{\mathcal {Y}}\) over X such that \(\mathcal {Y}\subseteq \tau _{\mathcal {Y}}\).

  3. 3.

    Attack edges involving the empty set are not drawn.

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Acknowledgement

The author is grateful to Fernando R. Velázquez-Quesada for his valuable feedback on the first draft of this paper and to the three anonymous referees of this paper for their comments and remarks.

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Authors and Affiliations

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

    Chenwei Shi

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  1. Chenwei Shi
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Correspondence to Chenwei Shi .

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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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Shi, C. (2019). Knowledge in Topological Argumentation Models. 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_21

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  • DOI: https://doi.org/10.1007/978-3-662-60292-8_21

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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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