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Beyond Modalities: Sufficiency and Mixed Algebras

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Relational Methods for Computer Science Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 65))

Abstract

In [24] a generalisation of relation algebras to Boolean algebras with normal and additive operators is introduced. These operators are the counterparts to the modal operators of possibility. In this paper we introduce a class of Boolean algebras with co-normal and co-additive operators referred to as sufficiency operators. They are the algebraic counterpart to the logical sufficiency operators introduced in [17] for an extension of modal logics. Next, we define a class of mixed algebras i.e., Boolean algebras with an additional modal operator and a sufficiency operator. We study representation and duality theory for these new classes of algebras. The motivation for those algebras comes from the problems of reasoning with incomplete information and spatial reasoning.

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Author information

Authors and Affiliations

  1. School of Information and Software Engineering, University of Ulster at Jordanstown, Newtownabbey, BT 37 OQB, N.Ireland

    Ivo Düntsch

  2. Institute of Telecommunications, Szachowa 1, 04-894, Warszawa, Poland

    Ewa Orłowska

Authors
  1. Ivo Düntsch
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  2. Ewa Orłowska
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Editor information

Editors and Affiliations

  1. Institute of Telecommunications, ul. Szachowa 1, 04-894, Warsaw, Poland

    Ewa Orłowska

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

    Andrzej Szałas

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© 2001 Springer-Verlag Berlin Heidelberg

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Düntsch, I., Orłowska, E. (2001). Beyond Modalities: Sufficiency and Mixed Algebras. In: Orłowska, E., Szałas, A. (eds) Relational Methods for Computer Science Applications. Studies in Fuzziness and Soft Computing, vol 65. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1828-4_16

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  • DOI: https://doi.org/10.1007/978-3-7908-1828-4_16

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-00362-6

  • Online ISBN: 978-3-7908-1828-4

  • eBook Packages: Springer Book Archive

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