In proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic arithmetic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so-called System T. It was developed by Kurt Gödel to provide a consistency proof of arithmetic. The name of the interpretation comes from the journal Dialectica, where Gödel's paper was published in a 1958 special issue dedicated to Paul Bernays on his 70th birthday. (Wikipedia).
Giuseppe Rosolini: Triposes and Gödel's Dialectica Interpretation
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: In previous joint work with B. Biering, L. Birkedal, C. Butz, J.M.E. Hyland, J. van Oosten, and T. Streicher, the problem of a semantic presentation of the functional int
From playlist Workshop: "Proofs and Computation"
Paulo Oliva: On a Dialectica like version of Kleene numerical realizability
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Kleene's original notion of realizability (1945) makes use of all (partial) computable functions as potential realisers. Later Kreisel (1959) presented a "modified" notio
From playlist Workshop: "Proofs and Computation"
Makoto Fujiwara: Bar theorem and bar recursion for continuous functions with continuous modulus
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: (joint work with Tatsuji Kawai) Bar induction is originally discussed by L. E. J. Brouwer under the name of “bar theorem” in his intuitionistic mathematics but first formali
From playlist Workshop: "Constructive Mathematics"
Hugo Herbelin: Computing with Markov's principle
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Computing with Markov's principle via a realizability interpretation is standard, using unbounded search as in Kleene's realizability or by selecting the first valid wit
From playlist Workshop: "Proofs and Computation"
Amir Tabatabai Mining the Surface: Proof mining in the bounded world
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: A computational flow is a pair consisting of a sequence of computational problems of a certain sort and a sequence of computational reductions among them. In this talk we
From playlist Workshop: "Proofs and Computation"
Exponent Law: Geometric Interpretation
GeoGebra Resource Link: https://www.geogebra.org/m/wnnsr3en
From playlist Algebra 1: Dynamic Interactives!
Simplifying a rational expression by factoring
Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational
From playlist Simplify Rational Expressions
Simplify a rational expression
Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational
From playlist Simplify Rational Expressions
Simplifying a rational expression by factoring
Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational
From playlist Simplify Rational Expressions
Simplify an expression by applying quotient rule of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
Summary Simplifying rational expressions
Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational
From playlist Simplify Rational Expressions
What are multiplicative inverses
👉 Learn how to simplify mathematics expressions. A mathematis expression is a finite combination of numbers and symbols formed following a set of operations or rules. To simplify a mathematics expression means to reduce the expression into simpler form. Given a mathematics expression, to
From playlist Simplify Expressions Using Order of Operations
Law of Exponents: Geometric Illustration
Dynamic GEOMETRIC ILLUSTRATION of a popular LAW OF EXPONENTS. Parameters modifiable: geogebra.org/m/wnnsr3en. #GeoGebra #MTBoS #ITeachMath #EdTech #math #maths #EdTech #algebra #geometry #MSMath #HSMath #MathEdTech
From playlist Algebra 1: Dynamic Interactives!
How a video game designer is blurring the lines separating the real from the virtual
Lovers of video games have long embraced Gran Turismo, one of the most popular racing simulators in the world. The game, which runs on Sony’s PlayStation console, is so realistic that it has been used to train real race car drivers. Currently, Gran Turismo’s parent company, Polyphony Digit
From playlist CARS Open Garage Talk lecture series
Cross examination by prosecution
From playlist UNSW Law
Presuppositionalism and Natural Theology: A Critical Analysis
A guest reading by Riverrun of "Presuppositionalism and Natural Theology: A Critical Analysis of the Presuppositional Challenge to Natural Theology" by Prof. David Haines. Full text: https://www.academia.edu/17323489/PRESUPPOSITIONALISM_AND_NATURAL_THEOLOGY
From playlist Philosophy
From playlist UNSW Law
Simplify rational expression using the rules of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
Learn the basics for simplifying an expression using the rules of exponents
👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat
From playlist Simplify Using the Rules of Exponents | Quotient Rule
Interpretable Neural Networks for Panel Data Analysis in Economics | AISC
For slides and more information on the paper, visit https://ai.science/e/interpretable-neural-networks-for-panel-data-analysis-in-economics--fr9lyZxVFVPjoniQb1uR Speaker: Yucheng Yang; Host: Jiri Stodulka Motivation: Even though deep learning and sufficient amount of data may lead to st
From playlist ML in Economics