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Combining and representing logical systems using model-theoretic parchments

  • Till Mossakowski
  • Andrzej Tarlecki
  • Wiesław Pawłowski
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1376)

Abstract

The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. We adopt the model-theoretic view of logic as captured in the notions of institution and of parchment (an algebraic way of presenting institutions). We propose a new, modified notion of parchment together with parchment morphisms and representations. In contrast to the original parchment definition and our earlier work, in model-theoretic parchments introduced here the universal semantic structure is distributed over individual signatures and models. We lift formal properties of the categories of institutions and their representations to this level: the category of model-theoretic parchments is complete, and their representations may be put together using categorical limits as well. However, model-theoretic parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessary invention for combination of various logical features may be introduced either on an ad hoc basis or via representations in a universal logic.

Keywords

Modal Logic Natural Transformation Logical System Abstract Syntax Semantic Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Till Mossakowski
    • 1
  • Andrzej Tarlecki
    • 2
    • 3
  • Wiesław Pawłowski
    • 4
  1. 1.Department of Computer ScienceUniversity of BremenBremen
  2. 2.Institute of InformaticsWarsaw UniversityPoland
  3. 3.Institute of Computer SciencePolish Academy of SciencesWarsaw
  4. 4.Institute of Computer SciencePolish Academy of SciencesGdańsk

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