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On the Structure of the Simulation Order of Proof Systems

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Mathematical Foundations of Computer Science 2002 (MFCS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2420))

Abstract

We examine the degree structure of the simulation relation on the proof systems for a set L. As observed, this partial order forms a distributive lattice. A greatest element exists iff L has an optimal proof system. In case L is infinite there is no least element, and the class of proof systems for L is not presentable. As we further show the simulation order is dense. In fact any partial order can be embedded into the interval determined by two proof systems f and g such that f simulates g but g does not simulate f. Finally we obtain that for any non-optimal proof system h an infinite set of proof systems that are pairwise incomparable with respect simulation and that are also incomparable to h.

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Authors and Affiliations

  1. Abteilung Theoretische Informatik, Universität Ulm, 89069, Ulm, Germany

    Jochen Messner

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  1. Jochen Messner
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Editors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland

    Krzysztof Diks  & Wojciech Rytter  & 

  2. Department of Computer Science, Liverpool University, Peach Street, Liverpool, L69 7ZF, UK

    Wojciech Rytter

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© 2002 Springer-Verlag Berlin Heidelberg

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Messner, J. (2002). On the Structure of the Simulation Order of Proof Systems. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_48

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  • DOI: https://doi.org/10.1007/3-540-45687-2_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44040-6

  • Online ISBN: 978-3-540-45687-2

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