Metalogic | Formal languages | Formal systems

Formal system

A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined system of abstract thought. The term formalism is sometimes a rough synonym for formal system, but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. (Wikipedia).

Video thumbnail

What Are Reactive Systems?

Reactive Systems use a high-performance software architecture. They are resilient under stress, and their reactive design allows them to scale elastically to meet demand. The reactive design approach allows the creation of more complex, more flexible systems and forms the basis for some of

From playlist Software Engineering

Video thumbnail

Quantum Mechanics -- a Primer for Mathematicians

Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w

From playlist Mathematics

Video thumbnail

SYN103 - Grammar (Overview)

There is a great deal of confusion about the term 'grammar'. Most people associate with it a book written about a language. In fact, there are various manifestations of this traditional term: presecriptive, descriptive and reference grammar. In theoretical linguistics, grammars are theory

From playlist VLC107 - Syntax: Part II

Video thumbnail

Linear Algebra - Lecture 10 - Homogeneous Linear Systems

In this lecture, we define "homogeneous" linear systems, and discuss how to find the solutions to these systems in parametric vector form.

From playlist Linear Algebra Lectures

Video thumbnail

Type Systems - Vladimir Voevodsky

Vladimir Voevodsky Institute for Advanced Study November 21, 2012

From playlist Mathematics

Video thumbnail

Writing a Formal Business Letter

In this video, you’ll learn more about writing a formal business letter. Visit https://www.gcflearnfree.org/business-communication/how-to-write-a-formal-business-letter/1/ for our text-based lesson. This video includes information on: • The format and structure of business letters • Uses

From playlist Communication in the Workplace

Video thumbnail

Formal Definition of a Function using the Cartesian Product

Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid

From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)

Video thumbnail

Operating system for beginners || Operating system basics

An operating system (OS) is system software that manages computer hardware, software resources, and provides common services for computer programs. Time-sharing #operating_systems schedule tasks for efficient use of the system and may also include accounting software for cost allocation o

From playlist Operating System

Video thumbnail

Mathematical modeling of evolving systems

Discover the multidisciplinary nature of the dynamical principles at the core of complexity science. COURSE NUMBER: CAS 522 COURSE TITLE: Dynamical Systems LEVEL: Graduate SCHOOL: School of Complex Adaptive Systems INSTRUCTOR: Enrico Borriello MODE: Online SEMESTER: Fall 2021 SESSION:

From playlist What is complex systems science?

Video thumbnail

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

Video thumbnail

10/25/19, Fabian Immler

Fabian Immler, Carnegie Mellon University Formal mathematics and a proof of chaos Formal proof has been successfully applied to the verification of hardware and software systems. But formal proof is also applicable to mathematics: proofs can be checked with ultimate rigor and one can bui

From playlist Fall 2019 Kolchin Seminar in Differential Algebra

Video thumbnail

Séminaire Bourbaki - 21/06/2014 - 4/4 - Thierry COQUAND

Théorie des types dépendants et axiome d'univalence Cet exposé sera une introduction à la théorie des types dépendants et à l'axiome d'univalence. Cette théorie est une alternative à la théorie des ensembles comme fondement des mathématiques. Guidé par une interprétation d'un type comme u

From playlist Bourbaki - 21 juin 2014

Video thumbnail

Foundations of Mathematics and Homotopy Theory - Vladimir Voevodsky

Vladimir Voevodsky Institute for Advanced Study March 22, 2006 More videos on http://video.ias.edu

From playlist Mathematics

Video thumbnail

Kurt Gödel Centenary - Part I

Institute for Advanced Study November 17, 2006 Karl Sigmund (University of Vienna) Solomon Feferman (Stanford University) More videos on http://video.ias.edu

From playlist Kurt Gödel Centenary

Video thumbnail

3 - Kick-off afternoon : Thomas Hales, Formalizing the proof of the Kepler Conjecture

Thomas Hales (University of Pittsburgh): Formalizing the proof of the Kepler Conjecture

From playlist T2-2014 : Semantics of proofs and certified mathematics

Video thumbnail

What if Current Foundations of Mathematics are Inconsistent? | Vladimir Voevodsky

Vladimir Voevodsky, Professor, School of Mathematics, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/voevodsky In this lecture, Professor Vladimir Voevodsky begins with Gödel's second incompleteness theorem to discuss the possibility that the formal theory of f

From playlist Mathematics

Video thumbnail

First Author Interview: AI & formal math (Formal Mathematics Statement Curriculum Learning)

#openai #math #imo This is an interview with Stanislas Polu, research engineer at OpenAI and first author of the paper "Formal Mathematics Statement Curriculum Learning". Watch the paper review here: https://youtu.be/lvYVuOmUVs8 OUTLINE: 0:00 - Intro 2:00 - How do you explain the big pub

From playlist Applications of ML

Video thumbnail

Live CEOing Ep 28: Proofs in the Wolfram Language

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

From playlist Behind the Scenes in Real-Life Software Design

Video thumbnail

Univalent Foundations Seminar - Steve Awodey

Steve Awodey Carnegie Mellon University; Member, School of Mathematics November 19, 2012 For more videos, visit http://video.ias.edu

From playlist Mathematics

Related pages

George Boole | Euclidean geometry | Interpretation (logic) | Gottlob Frege | Theorem | Gödel's incompleteness theorems | Propositional calculus | Lambda calculus | Completeness (logic) | Non-standard model of arithmetic | Formal grammar | Model theory | Theory (mathematical logic) | David Hilbert | Mathematical proof | Axiom schema | Predicate calculus | Well-formed formula | Formal language | Peano axioms | Decidability (logic) | Symbol (formal) | Modal logic | Mathematics | Set (mathematics) | Stephen Cole Kleene | Metatheorem | Axiomatic system | Formal proof | Generative grammar | Abstract structure | Axiom | Semantics of logic | Domain of discourse | Mathematical logic | Rule of inference | Bra–ket notation | Deductive reasoning | Soundness | First-order logic | Philosophy of mathematics | Metamathematics | Metalanguage | String (computer science)