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Hybridization of Institutions

  • Manuel A. Martins
  • Alexandre Madeira
  • Răzvan Diaconescu
  • Luís S. Barbosa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6859)

Abstract

Modal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for naming states in models. Actually, hybrid logics have recently regained interest, resulting in a number of new results and techniques as well as applications to software specification.

In this context, the first contribution of this paper is an attempt to ‘universalize’ the hybridization idea. Following the lines of [15], where a method to modalize arbitrary institutions is presented, the paper introduces a method to hybridize logics at the same institution-independent level. The method extends arbitrary institutions with Kripke semantics (for multi-modalities with arbitrary arities) and hybrid features. This paves the ground for a general result: any encoding (expressed as comorphism) from an arbitrary institution to first order logic (\(\mathcal{FOL}\)) determines a comorphism from its hybridization to \(\mathcal{FOL}\). This second contribution opens the possibility of effective tool support to specification languages based upon logics with hybrid features.

Keywords

Institution theory hybrid logic formal specification 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Manuel A. Martins
    • 1
  • Alexandre Madeira
    • 1
    • 2
    • 4
  • Răzvan Diaconescu
    • 3
  • Luís S. Barbosa
    • 2
  1. 1.Department of MathematicsUniversity of AveiroPortugal
  2. 2.Department of InformaticsMinho UniversityPortugal
  3. 3.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyRomania
  4. 4.Critical Software S.A.Portugal

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