An institutional version of Gödel's completeness theorem

Authors:
Marius Petria
Affiliations:
University of Edinburgh
Venue:
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Year:
2007

Citing 3
Cited 0

Bits and pieces of the theory of institutions

Proceedings of a tutorial and workshop on Category theory and computer programming
Institutions: abstract model theory for specification and programming

Journal of the ACM (JACM)
Institution-independent Model Theory

Institution-independent Model Theory

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Abstract

Gödel's famous result about the completeness of first order deduction can be cast in the general framework of institutions. For this we use Henkin's method of proving completeness which is very generic and has been exploited over time by producing similar proofs of completeness for various logical systems. This paper sets out a general framework with the purpose to incorporates many of these proofs as examples. As a consequence of this abstraction, the completeness theorem becomes available for many "first order" logical systems that appear in the area of logic or computer science.