continuous logic

Continuous logic is a logic whose truth values can take continuous values in $[0,1]$. 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.

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)