Theoretical computer science | Systems of formal logic | Categorical logic

Categorical logic

Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor. The categorical framework provides a rich conceptual background for logical and type-theoretic constructions. The subject has been recognisable in these terms since around 1970. (Wikipedia).

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Logic: The Structure of Reason

As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be

From playlist Logic & Philosophy of Mathematics

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Introduction to Predicate Logic

This video introduces predicate logic. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Logic - Types of Statements

An introduction to the general types of logic statements

From playlist Geometry

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Olivia Caramello - 2/4 ntroduction to categorical logic, classifying toposes...

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From playlist Topos à l'IHES

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Introduction to the Cardinality of Sets and a Countability Proof

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From playlist Set Theory

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Model Theory - part 08 - Semantics pt 2

This is the second video on Semantics. I used Caramello and Awodey's notes on this.

From playlist Model Theory

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Clemens Koppensteiner: T-structures from categorical actions

Abstract: T-structures on derived categories of coherent sheaves are an important tool to encode both representation-theoretic and geometric information. Unfortunately there are only a limited amount of tools available for the constructions of such t-structures. We show how certain geometr

From playlist Algebraic and Complex Geometry

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Logic - Negation

An introduction to the logical process of negation

From playlist Geometry

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The online ceremony celebrating the official launch of the Huawei Young Talents Program at the Institut des Hautes Etudes Scientifiques was held on 6 November 2020. This program aims to support the work of talented researchers in mathematics and theoretical physics at the beginning of thei

From playlist Huawei Young Talents Program - November 2020

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Olivia Caramello - 1/4 Introduction to Grothendieck toposes

This course provides an introduction to the theory of Grothendieck toposes from a meta-mathematical point of view. It presents the main classical approaches to the subject (namely, toposes as generalized spaces, toposes as mathematical universes and toposes as classifiers of models of firs

From playlist Olivia Caramello - Introduction to Grothendieck toposes

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Towards elementary infinity-toposes - Michael Shulman

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From playlist Mathematics

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Formal Logic

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From playlist Summer of Math Exposition 2 videos

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Introduction to Philosophy and Logic

Humans are on a quest to understand the world around us. How did this quest begin? What are the tools we use to gather knowledge? How do we know what is possible to know? What do we mean when using words like ethics, ontology, metaphysics, aesthetics, and logic? This series is going to get

From playlist Philosophy/Logic

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LambdaConf 2015 - Type Theory and its Meaning Explanations Jon Sterling

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From playlist LambdaConf 2015

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Saharon Shelah : Categoricity of atomic classes in small cardinals, in ZFC

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From playlist Logic and Foundations

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Beginner's Guide to Kant's Moral Philosophy

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From playlist A-Level Philosophy

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R - Data Screening 1 Accuracy Checks

Recorded: Fall 2015 Lecturer: Dr. Erin M. Buchanan This video covers how to check your data for accuracy errors and how to fix those errors using several different subsetting rules in R. Lecture materials and assignment available at statisticsofdoom.com. https://statisticsofdoom.com/page

From playlist Learn R + Statistics

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Model Theory - part 07 - Semantics pt 1

This is the first video on semantics.

From playlist Model Theory

Related pages

Category of sets | Interpretation (logic) | System F | Theoretical computer science | Untyped lambda calculus | Model theory | Metalogic | Theory (mathematical logic) | History of topos theory | Topos | Equational logic | Fibred category | Mathematics | Equivalence of categories | Category theory | Category (mathematics) | Functor | Type theory | Mathematical logic | Cartesian closed category | Intuitionistic logic | Universal property | Simply typed lambda calculus | Effective topos