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(Dual) Hoops Have Unique Halving

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Automated Reasoning and Mathematics

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7788))

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Abstract

Continuous logic extends the multi-valued Łukasiewicz logic by adding a halving operator on propositions. This extension is designed to give a more satisfactory model theory for continuous structures. The semantics of these logics can be given using specialisations of algebraic structures known as hoops and coops. As part of an investigation into the metatheory of propositional continuous logic, we were indebted to Prover9 for finding proofs of important algebraic laws.

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Authors and Affiliations

  1. School of Electronic Engineering and Computer Science, Queen Mary University of London, Mile End Road, London, E1 4NS, UK

    Rob Arthan & Paulo Oliva

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  1. Rob Arthan
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  2. Paulo Oliva
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Editors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Verona, 37134, Verona, Italy

    Maria Paola Bonacina

  2. Artificial Intelligence Center, SRI International, 333 Ravenswood Avenue, 94025, Menlo Park, CA, USA

    Mark E. Stickel

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Arthan, R., Oliva, P. (2013). (Dual) Hoops Have Unique Halving. In: Bonacina, M.P., Stickel, M.E. (eds) Automated Reasoning and Mathematics. Lecture Notes in Computer Science(), vol 7788. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36675-8_9

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  • DOI: https://doi.org/10.1007/978-3-642-36675-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36674-1

  • Online ISBN: 978-3-642-36675-8

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