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What is a Logic?

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Logica Universalis

Abstract

This paper builds on the theory of institutions, a version of abstract model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual. A natural equivalence relation on institutions is defined such that its equivalence classes are logics. Several invariants are defined for this equivalence, including a Lindenbaum algebra construction, its generalization to a Lindenbaum category construction that includes proofs, and model cardinality spectra; these are used in some examples to show logics inequivalent. Generalizations of familiar results from first order to arbitrary logics are also discussed, including Craig interpolation and Beth definability.

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Author information

Authors and Affiliations

  1. Universität Bremen, Germany

    Till Mossakowski

  2. University of California at San Diego, USA

    Joseph Goguen

  3. Institute of Mathematics, Romanian Academy, Bucharest, Romania

    RĂzvan Diaconescu

  4. Institute of Informatics, Warsaw University, Warsaw

    Andrzej Tarlecki

  5. Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland

    Andrzej Tarlecki

Authors
  1. Till Mossakowski
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  2. Joseph Goguen
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  3. RĂzvan Diaconescu
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  4. Andrzej Tarlecki
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Editor information

Editors and Affiliations

  1. Institute of Logic, University of Neuchâtel, Espace Louis Agassiz 1, 2000, Neuchâtel, Switzerland

    Jean-Yves Beziau

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Mossakowski, T., Goguen, J., Diaconescu, R., Tarlecki, A. (2005). What is a Logic?. In: Beziau, JY. (eds) Logica Universalis. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7304-0_7

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