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- W2912705627 abstract "Using the category of metric spaces as a template, we develop a metric analogue of the categorical semantics of classical/intuitionistic logic, and show that the natural notion of predicate in this continuous semantics is equivalent to the a priori separate notion of predicate in continuous logic, a logic which is independently well-studied by model theorists and which finds various applications. We show this equivalence by exhibiting the real interval [0,1] in the category of metric spaces as a continuous subobject classifier giving a correspondence not only between the two notions of predicate, but also between the natural notion of quantification in the continuous semantics and the existing notion of quantification in continuous logic. Along the way, we formulate what it means for a given category to behave like the category of metric spaces, and afterwards show that any such category supports the aforementioned continuous semantics. As an application, we show that categories of presheaves of metric spaces are examples of such, and in fact even possess continuous subobject classifiers." @default.
- W2912705627 created "2019-02-21" @default.
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- W2912705627 date "2020-09-01" @default.
- W2912705627 modified "2023-10-14" @default.
- W2912705627 title "CATEGORICAL SEMANTICS OF METRIC SPACES AND CONTINUOUS LOGIC" @default.
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- W2912705627 doi "https://doi.org/10.1017/jsl.2020.44" @default.
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