Quantifiers and measures -- Tomáš Jakl & Luca Reggio
Duration: 1 hour 29 mins
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About this item
| Description: | (No description) |
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| Created: | 2020-04-01 18:13 |
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| Collection: | Online Workshop: Resources and Co-Resources: A Junction between Semantics and Descriptive Complexity |
| Publisher: | University of Cambridge |
| Copyright: | Tomáš Jakl & Luca Reggio |
| Language: | eng (English) |
| Abstract: | Traditionally, in categorical logic, first-order quantifiers are encoded as adjoints to the inclusion maps of the algebra of formulas in n free variables into the algebra of formulas in n+1 free variables. Hence, quantifiers correspond to a property of the inclusion maps. We depart from this standpoint and propose viewing quantification as a "construction". We discuss how, from this perspective, quantification can be dually understood as a space-of-measures construction. To illustrate these ideas, we draw from recent results obtained in collaboration with Mai Gehrke and Daniela Petrisan where the viewpoint of quantifiers as measures has been successfully applied in logic on words and finite model theory.
The talk is divided into two parts, one presented by Tomas Jakl and the other by Luca Reggio. slides - Luca: https://www.cst.cam.ac.uk/sites/www.cst.cam.ac.uk/files/reggio-cambridge-2020.pdf slides - Tomáš: https://www.cst.cam.ac.uk/sites/www.cst.cam.ac.uk/files/slides.pdf |
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