nLab
continuous logic

Idea

Continuous logic is a logic whose truth values can take continuous values in [0,1][0,1]. The main variant used in model theory is motivated by the model theory of Banach spaces and similar structures. The truth is interpreted as probability and there is a concept of random predicates.

References

Continuous logic is introduced in

  • C. W. Henson, J. Iovino, Ultraproducts in analysis in: Analysis and Logic, London Math. Soc. Lecture Note Series 262, Cambridge University Press 2002.

motivated by

  • Chen-Chung Chang, Jerome H. Keisler, Continuous Model Theory, Annals of Mathematics Studies 58, 1966.

A recent version is in

  • Itay Ben-Yacoov, Uncountable dense categoricity in cats, J. Symb. Logic 70, 829–860, 2005
  • I. Ben-Yacoov, Continuous first-order logic and logical stability, pdf
  • Itay Ben-Yaacov, Alex Usvyatsov. Logic of metric spaces and Hausdorff CATs
  • Itay Ben Yaacov, Alexander Berenstein, Ward C. Henson, Alexander Usvyatsov, Model Theory for metric structures, in Model Theory with Applications to Algebra and Analysis, Volume 2, Cambridge University Press, 2008, pdf
  • Alexander Berenstein, Andres Villaveces, Hilbert spaces with random predicates, pdf

A discussion of conceptual completeness in the setting of continuous logic is found in

  • Jean-Martin Albert, Bradd Hart. Metric logical categories and conceptual completeness for first order continuous logic pdf

An older and rather different system also called continuous logic of a Russian school is surveyed

  • Vitaly I. Levin, Basic concepts of continuous logic, Studies in logic grammar and rethoric, 11 (24) 2007, pdf

There is a version of abstract elementary classes in the setting of continuous logic, metric abstract elementary classes.

Revised on July 29, 2016 01:59:18 by Tim Porter (90.24.171.16)