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Abstract Cyclic Proofs

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Logic, Language, Information, and Computation (WoLLIC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13468))

Abstract

Cyclic proof systems permit derivations that are finite graphs in contrast to conventional derivation trees. The soundness of such proofs is ensured by a condition on the paths through the derivation graph, known as the global trace condition. To give a uniform treatment of such cyclic proof systems, Brotherston proposed an abstract notion of trace. We extend Brotherston’s approach into a category theoretical rendition of cyclic derivations, advancing the framework in two ways: First, we introduce activation algebras which allow for a more natural formalisation of trace conditions in extant cyclic proof systems. Second, accounting for the composition of trace information allows us to derive novel results about cyclic proofs, such as introducing the Ramsey trace condition.

This work was supported by the Knut and Alice Wallenberg Foundation [2020.0199, 2015.0179]; and the Swedish Research Council [2017-05111, 2016-03502].

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Authors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands

    Bahareh Afshari

  2. Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg, Gothenburg, Sweden

    Bahareh Afshari & Dominik Wehr

Authors
  1. Bahareh Afshari
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  2. Dominik Wehr
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Correspondence to Dominik Wehr .

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Editors and Affiliations

  1. Technische Universität Wien, Vienna, Austria

    Agata Ciabattoni

  2. University College London, London, UK

    Elaine Pimentel

  3. Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil

    Ruy J. G. B. de Queiroz

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Afshari, B., Wehr, D. (2022). Abstract Cyclic Proofs. In: Ciabattoni, A., Pimentel, E., de Queiroz, R.J.G.B. (eds) Logic, Language, Information, and Computation. WoLLIC 2022. Lecture Notes in Computer Science, vol 13468. Springer, Cham. https://doi.org/10.1007/978-3-031-15298-6_20

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  • DOI: https://doi.org/10.1007/978-3-031-15298-6_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-15297-9

  • Online ISBN: 978-3-031-15298-6

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