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A Mechanised Proof System for Relation Algebra Using Display Logic

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Logics in Artificial Intelligence (JELIA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1489))

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Abstract

We describe an implementation of the Display Logic calculus for relation algebra as an Isabelle theory. Our implementation is the first mechanisation of any display calculus. The inference rules of Display Logic are coded directly as Isabelle theorems, thereby guaranteeing the correctness of all derivations. Our implementation generalises easily to handle other display calculi. It also provides a useful interactive proof assistant for relation algebras.

We describe various tactics and derived rules developed for simplifying proof search, including an automatic cut-elimination procedure, and example theorems proved using Isabelle. We show how some relation algebraic theorems proved using our system can be put in the form of structural rules of Display Logic, facilitating later re-use. We then show how the implementation can be used to prove results comparing alternative formalizations of relation algebra from a proof-theoretic perspective.

Supported by the Defence Science and Technology Organization

Supported by an Australian Research Council QEII Fellowship

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Author information

Authors and Affiliations

  1. Department of Computer Science and Automated Reasoning Project, Australian National University, Canberra, Australia

    Jeremy E. Dawson & Rajeev Goré

Authors
  1. Jeremy E. Dawson
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  2. Rajeev Goré
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Maryland, College Park, Maryland, 20742, USA

    Jürgen Dix

  2. I.R.I.T. Université Paul Sabatier, 118 route de Narbonne, F-31062, Toulouse Cedex, France

    Luís Fariñas del Cerro

  3. Fachbereich 4: Informatik, Universität Koblenz, Rheinau 1, D-56075, Koblenz, Germany

    Ulrich Furbach

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© 1998 Springer-Verlag Berlin Heidelberg

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Dawson, J.E., Goré, R. (1998). A Mechanised Proof System for Relation Algebra Using Display Logic. In: Dix, J., del Cerro, L.F., Furbach, U. (eds) Logics in Artificial Intelligence. JELIA 1998. Lecture Notes in Computer Science(), vol 1489. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49545-2_18

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  • DOI: https://doi.org/10.1007/3-540-49545-2_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65141-3

  • Online ISBN: 978-3-540-49545-1

  • eBook Packages: Springer Book Archive

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