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Category Theory and Computer Science

Volume 1290 of the series Lecture Notes in Computer Science pp 177-196

Date:

Combining and representing logical systems

  • Till MossakowskiAffiliated withDepartment of Computer Science, University of Bremen Email author 
  • , Andrzej TarleckiAffiliated withInstitute of Informatics, Warsaw University and Institute of Computer Science, Polish Academy of Sciences
  • , Wieslaw PawłowskiAffiliated withInstitute of Computer Science, Polish Academy of Sciences

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Abstract

The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. Following Goguen and Burstall, we adopt the model-theoretic view of logic as captured in the notion of institution and of parchment (a certain algebraic way of presenting institutions).

We propose a modified notion of parchment together with a notion of parchment morphism and representation, respectively. We lift formal properties of the categories of institutions and their representations to this level: the category of parchments is complete, and parchment representations may be put together using categorical limits as well. However, parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessary invention for proper combination of various logical features may be introduced either on an ad hoc basis (when putting parchments together using limits in the category of parchments) or via representations in a universal logic (when parchment combination is driven by their representations).