Theoretical computer science | Systems of formal 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).
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
Introduction to Predicate Logic
This video introduces predicate logic. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
An introduction to the general types of logic statements
From playlist Geometry
IAML2.7: Categorical (nominal) attributes
From playlist Thinking about Data
Olivia Caramello - 2/4 ntroduction to categorical logic, classifying toposes...
Introduction to categorical logic, classifying toposes and the « bridge » technique Construction of classifying toposes for geometric theories. Duality between the subtoposes of the classifying topos of a geometric theory and the quotients of the theory. Transfer of topos‐the
From playlist Topos à l'IHES
Introduction to the Cardinality of Sets and a Countability Proof
Introduction to Cardinality, Finite Sets, Infinite Sets, Countable Sets, and a Countability Proof - Definition of Cardinality. Two sets A, B have the same cardinality if there is a bijection between them. - Definition of finite and infinite sets. - Definition of a cardinal number. - Discu
From playlist Set Theory
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
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
Huawei Young Talents Programme - Laurent Lafforgue
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
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
Towards elementary infinity-toposes - Michael Shulman
Vladimir Voevodsky Memorial Conference Topic: Towards elementary infinity-toposes Speaker: Michael Shulman Affiliation: University of San Diego Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
This video functions as a brief introduction to many different topics in formal logic. Notes on the Images: I looked into the legality of using images for this video a good deal and I've come to the conclusion that there is nothing in this video which could remotely imply these images ar
From playlist Summer of Math Exposition 2 videos
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
LambdaConf 2015 - Type Theory and its Meaning Explanations Jon Sterling
At the heart of intuitionistic type theory lies an intuitive semantics called the “meaning explanations." Crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer “proof” but “verification”. We’ll explore how type theories of this sort aris
From playlist LambdaConf 2015
Saharon Shelah : Categoricity of atomic classes in small cardinals, in ZFC
CONFERENCE Recording during the thematic meeting : « Discrete mathematics and logic: between mathematics and the computer science » the January 17, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks give
From playlist Logic and Foundations
Beginner's Guide to Kant's Moral Philosophy
A simple introduction to Kant’s Categorical Imperative and his deontological approach to ethics Subscribe! http://tinyurl.com/pr99a46 Guest Stars! Carly Toffle - http://tinyurl.com/zcngtcl Cameron Sanderson - http://tinyurl.com/jytlpu6 Patreon: http://www.patreon.com/PhilosophyTube Audi
From playlist A-Level Philosophy
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
Model Theory - part 07 - Semantics pt 1
This is the first video on semantics.
From playlist Model Theory