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International Conference on Concurrency Theory

CONCUR 2007: CONCUR 2007 – Concurrency Theory pp 197–211Cite as

Is Observational Congruence Axiomatisable in Equational Horn Logic?

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4703))

Abstract

It is well known that bisimulation on μ-expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features which go beyond pure equational Horn logic: either the rules are impure by involving non-equational side-conditions, or they are schematically infinitary like the congruence rule which is not Horn. It is an open question whether these complications cannot be avoided in the proof-theoretically and computationally clean and powerful setting of second-order equational Horn logic.

This paper presents a positive and a negative result regarding axiomatisability of observational congruence in equational Horn logic. Firstly, we show how Milner’s impure rule system can be reworked into a pure Horn axiomatisation that is complete for guarded processes. Secondly, we prove that for unguarded processes, both Milner’s and Bloom/Ésik’s axiomatisations are incomplete without the congruence rule, and neither system has a complete extension in rank 1 equational axioms. It remains open whether there are higher-rank equational axioms or Horn rules which would render Milner’s or Bloom/Ésik’s axiomatisations complete for unguarded processes.

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Authors and Affiliations

  1. Informatics Theory Group, University of Bamberg, Germany

    Michael Mendler

  2. Department of Computer Science, University of York, UK

    Gerald Lüttgen

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  1. Michael Mendler
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  2. Gerald Lüttgen
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Luís Caires Vasco T. Vasconcelos

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Mendler, M., Lüttgen, G. (2007). Is Observational Congruence Axiomatisable in Equational Horn Logic?. In: Caires, L., Vasconcelos, V.T. (eds) CONCUR 2007 – Concurrency Theory. CONCUR 2007. Lecture Notes in Computer Science, vol 4703. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74407-8_14

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  • DOI: https://doi.org/10.1007/978-3-540-74407-8_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74406-1

  • Online ISBN: 978-3-540-74407-8

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