| Publication type: |
Article in Proceedings |
| Author: |
Till Mossakowski, Joseph Goguen, Razvan Diaconescu, Andrzej Tarlecki |
| Editor: |
Jean-Yves Beziau |
| Title: |
What is a Logic? (revised version) |
| Book / Collection title: |
Logica Universalis |
| Page(s): |
111 – 133 |
| Number: |
second edition |
| Year published: |
2007 |
| Publisher: |
Birkhäuser |
| 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. |
| Internet: |
http://dx.doi.org/10.1007/978-3-7643-8354-1_7 |
| PDF Version: |
http://www.informatik.uni-bremen.de/~till/papers/07-nel.pdf |
| Status: |
Reviewed |
| Last updated: |
01. 02. 2008 |
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