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Proof Search on Bilateralist Judgments over Non-deterministic Semantics

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12842))

Abstract

The bilateralist approach to logical consequence maintains that judgments of different qualities should be taken into account in determining what-follows-from-what. We argue that such an approach may be actualized by a two-dimensional notion of entailment induced by semantic structures that also accommodate non-deterministic and partial interpretations, and propose a proof-theoretical apparatus to reason over bilateralist judgments using symmetrical two-dimensional analytical Hilbert-style calculi. We also provide a proof-search algorithm for finite analytic calculi that runs in at most exponential time, in general, and in polynomial time when only rules having at most one formula in the succedent are present in the concerned calculus.

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Notes

  1. 1.

    Whether monadicity of a –matrix is decidable is still an open problem.

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Acknowledgements

V. Greati and J. Marcos acknowledge support from CAPES (Brasil)—Finance Code 001 and CNPq (Brasil), respectively. S. Marcelino’s research was done under the scope of Project UIDB/50008/2020 of Instituto de Telecomunicações (IT), financed by the applicable framework (FCT/MEC through national funds and cofunded by FEDER-PT2020).

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Authors and Affiliations

  1. Universidade Federal do Rio Grande do Norte, Natal, Brazil

    Vitor Greati & João Marcos

  2. Instituto de Telecomunicações, Lisboa, Portugal

    Sérgio Marcelino

Authors
  1. Vitor Greati
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  2. Sérgio Marcelino
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  3. João Marcos
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Corresponding author

Correspondence to Vitor Greati .

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Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Anupam Das

  2. University of Genoa, Genoa, Italy

    Sara Negri

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Greati, V., Marcelino, S., Marcos, J. (2021). Proof Search on Bilateralist Judgments over Non-deterministic Semantics. In: Das, A., Negri, S. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2021. Lecture Notes in Computer Science(), vol 12842. Springer, Cham. https://doi.org/10.1007/978-3-030-86059-2_8

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  • DOI: https://doi.org/10.1007/978-3-030-86059-2_8

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-86059-2

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