A Generalized Proof-Theoretic Approach to Logical Argumentation Based on Hypersequents

A. Borg, Christian Straßer, Ofer Arieli

    Research output: Contribution to journalArticleAcademicpeer-review

    Abstract

    In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the known weaknesses of logical argumentation frameworks and to prove several desirable properties of the entailments that are induced by the extended (hypersequent-based) frameworks. It also allows us to incorporate as the deductive base of our formalism some well-known logics (like the intermediate logic LC, the modal logic S5, and the relevance logic RM), which lack cut-free sequent calculi, and so are not adequate for standard sequent-based argumentation. We show that hypersequent-based argumentation yields robust defeasible variants of these logics, with many desirable properties.
    Original languageEnglish
    Pages (from-to)167-238
    Number of pages72
    JournalStudia Logica
    Volume109
    Issue number1
    Early online date2020
    DOIs
    Publication statusPublished - Feb 2021

    Bibliographical note

    Funding Information:
    We thank the reviewers for their helpful comments. The first two authors are supported by a Sofja Kovalevskaja award of the Alexander von Humboldt Foundation, funded by the German Ministry for Education and Research. The third author is supported by the Israel Science Foundation (Grants Nos.?817/15 and?550/19).

    Funding Information:
    We thank the reviewers for their helpful comments. The first two authors are supported by a Sofja Kovalevskaja award of the Alexander von Humboldt Foundation, funded by the German Ministry for Education and Research. The third author is supported by the Israel Science Foundation (Grants Nos. 817/15 and 550/19).

    Publisher Copyright:
    © 2020, The Author(s).

    Keywords

    • Defeasible reasoning
    • Hypersequents
    • Logical argumentation
    • Proof systems

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