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What is a Logic?

In: Logica Universalis

Author

Listed:
  • Till Mossakowski

    (Universität Bremen)

  • Joseph Goguen

    (University of California at San Diego)

  • RĂzvan Diaconescu

    (Romanian Academy, Institute of Mathematics)

  • Andrzej Tarlecki

    (Warsaw University, Institute of Informatics
    Polish Academy of Sciences, Institute of Computer Science)

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.

Suggested Citation

  • Till Mossakowski & Joseph Goguen & RĂzvan Diaconescu & Andrzej Tarlecki, 2005. "What is a Logic?," Springer Books, in: Jean-Yves Beziau (ed.), Logica Universalis, pages 113-133, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7304-7_7
    DOI: 10.1007/3-7643-7304-0_7
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