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Refutation Systems: An Overview and Some Applications to Philosophical Logics

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Knowledge, Proof and Dynamics

Part of the book series: Logic in Asia: Studia Logica Library ((LIAA))

Abstract

Refutation systems are systems of formal, syntactic derivations, designed to derive the non-valid formulas or logical consequences of a given logic. Here we provide an overview with comprehensive references on the historical development of the theory of refutation systems and discuss some of their applications to philosophical logics.

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Notes

  1. 1.

    As noted in Wybraniec-Skardowska (2018), for introducing the concept of formal rejection, Łukasiewicz was apparently influenced by Brentano, who was probably the first to consider on a par the two kinds of judgment, viz., acceptance and rejection, and to use a pair of symbols, \(+\) and −, to syntactically distinguish between them.

  2. 2.

    This reference is imported from other sources, albeit none of the authors have seen this technical report and it appears to be currently inaccessible in the internet.

  3. 3.

    For background on tableau methods for non-classical logics we refer the reader to Goré (1999).

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Acknowledgements

The work of Valentin Goranko was partly supported by a research grant 2015-04388 of the Swedish Research Council. Gabriele Pulcini thankfully acknowledges the support from the Dutch Research Council (NWO) through the Open Competition-SSH project 406.18.TW.009 “A Sentence Uttered Makes a World Appear—Natural Language Interpretation as Abductive Model Generation”.

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Authors and Affiliations

  1. Stockholm University, Stockholm, Sweden

    Valentin Goranko

  2. University of Johannesburg (Visiting Professorship), Johannesburg, South Africa

    Valentin Goranko

  3. University of Amsterdam, Amsterdam, The Netherlands

    Gabriele Pulcini

  4. University of Zielona Góra, Zielona Góra, Poland

    Tomasz Skura

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  1. Valentin Goranko
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  3. Tomasz Skura
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Correspondence to Valentin Goranko .

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

    Fenrong Liu

  2. Japan Advanced Institute of Science and Technology, Kanazawa, Japan

    Hiroakira Ono

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

    Junhua Yu

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Goranko, V., Pulcini, G., Skura, T. (2020). Refutation Systems: An Overview and Some Applications to Philosophical Logics. In: Liu, F., Ono, H., Yu, J. (eds) Knowledge, Proof and Dynamics. Logic in Asia: Studia Logica Library. Springer, Singapore. https://doi.org/10.1007/978-981-15-2221-5_9

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