Mathematical logic | Metalogic | Proof theory

Proof theory

Proof theory is a major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also focuses on applications in computer science, linguistics, and philosophy. (Wikipedia).

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Proofs by contradiction -- Proofs

This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

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Introduction to Common Mathematical Proof Methods

This video introduces the common methods of mathematical proofs and provides a basic example of a direct proof. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Geometry: Ch 5 - Proofs in Geometry (5 of 58) How to Proof Proofs

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is and how to proof proofs in geometry. Next video in this series can be seen at: https://youtu.be/xuWliQ6CHpw

From playlist GEOMETRY 5 - PROOFS IN GEOMETRY

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Review of set theory -- Proofs

This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

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SImple proofs and their variations -- Proofs

This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

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Proof: a³ - a is always divisible by 6 (2 of 2: Proof by exhaustion)

More resources available at www.misterwootube.com

From playlist The Nature of Proof

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Introduction to Direct Proofs: If n is even, then n squared is even

This video introduces the mathematical proof method of direct proof provides an example of a direct proof. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Haniel Barbosa - Better SMT proofs for certifying compliance and correctness - IPAM at UCLA

Recorded 14 February 2023. Haniel Barbosa of Universidade Federal de Minas Gerais in Belo Horizonte presents "Better SMT proofs for certifying compliance and correctness" at IPAM's Machine Assisted Proofs Workshop. Abstract: SMT solvers can be hard to trust, since it generally means assumi

From playlist 2023 Machine Assisted Proofs Workshop

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A Computer-Checked Proof that the Fundamental Group of the Circle is the Integers - Daniel Licata

Daniel Licata Carnegie Mellon University; Member, School of Mathematics November 26, 2012 This talk is designed for a general mathematical audience; no prior knowledge of type theory is presumed. One of the main goals for the special year on univalent foundations is the development of a l

From playlist Mathematics

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Foundations S2 - Seminar 2 - The geometric part

A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. This season the focus is on the proof of the Ax-Grothendieck theorem: an injective polynomial function from affine space (over the complex numbers) to itself is surjective. This week Will proved the the

From playlist Foundations seminar

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Type theory and formalization of mathematics - Anders Mörtberg

Short Talks by Postdoctoral Members Anders Mörtberg - September 28, 2015 http://www.math.ias.edu/calendar/event/88254/1443464100/1443465000 More videos on http://video.ias.edu

From playlist Short Talks by Postdoctoral Members

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Séminaire Bourbaki - 21/06/2014 - 3/4 - Thomas C. HALES

Developments in formal proofs A for mal proof is a proof that can be read and verified by computer, directly from the fundamental rules of logic and the foundational axioms of mathematics. The technology behind for mal proofs has been under development for decades and grew out of efforts i

From playlist Bourbaki - 21 juin 2014

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Homotopy Group - (1)Dan Licata, (2)Guillaume Brunerie, (3)Peter Lumsdaine

(1)Carnegie Mellon Univ.; Member, School of Math, (2)School of Math., IAS, (3)Dalhousie Univ.; Member, School of Math April 11, 2013 In this general survey talk, we will describe an approach to doing homotopy theory within Univalent Foundations. Whereas classical homotopy theory may be des

From playlist Mathematics

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On the Setoid Model of Type Theory - Erik Palmgren

Erik Palmgren University of Stockholm October 18, 2012 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Live CEOing Ep 178: Language Design in Wolfram Language

Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Language Design in the Wolfram Language.

From playlist Behind the Scenes in Real-Life Software Design

Related pages

Richard Dedekind | Mathematical object | Giuseppe Peano | Intuitionistic type theory | Natural deduction | Relevance logic | Proof (truth) | Solomon Feferman | Syntax (logic) | Gottlob Frege | Substructural logic | Theorem | Combinatorial proof | Gödel's incompleteness theorems | Japaridze's polymodal logic | Typed lambda calculus | Hilbert's program | Zorn's lemma | Reverse mathematics | Recursive data type | Ordinal analysis | Dialectica interpretation | Löb's theorem | Montague grammar | Proof mining | Analytic proof | Automated theorem proving | Arithmetical hierarchy | Hilbert system | David Hilbert | Model theory | Mathematical proof | Theory (mathematical logic) | Transfinite induction | Grundlagen der Mathematik | Proof complexity | Sequent calculus | Provability logic | Finitary | Focused proof | Interpretability logic | Modal logic | Alan Turing | Curry–Howard correspondence | Linear logic | Proof net | Diagonal lemma | Real number | Structural proof theory | Categorial grammar | Tree (data structure) | Axiom | Intermediate logic | Hao Wang (academic) | Mathematical logic | Type theory | Ω-consistent theory | Cartesian closed category | Intuitionistic logic | Cut-elimination theorem | Rule of inference | Stanisław Jaśkowski | Bertrand Russell | Classical logic | Self-verifying theories | Jon Barwise