Automated theorem proving | Logical calculi | Proof theory
In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology is inferred from other conditional tautologies on earlier lines in a formal argument according to rules and procedures of inference, giving a better approximation to the natural style of deduction used by mathematicians than to David Hilbert's earlier style of formal logic, in which every line was an unconditional tautology. More subtle distinctions may exist; for example, propositions may implicitly depend upon non-logical axioms. In that case, sequents signify conditional theorems in a first-order language rather than conditional tautologies. Sequent calculus is one of several extant styles of proof calculus for expressing line-by-line logical arguments. * Hilbert style. Every line is an unconditional tautology (or theorem). * Gentzen style. Every line is a conditional tautology (or theorem) with zero or more conditions on the left. * Natural deduction. Every (conditional) line has exactly one asserted proposition on the right. * Sequent calculus. Every (conditional) line has zero or more asserted propositions on the right. In other words, natural deduction and sequent calculus systems are particular distinct kinds of Gentzen-style systems. Hilbert-style systems typically have a very small number of inference rules, relying more on sets of axioms. Gentzen-style systems typically have very few axioms, if any, relying more on sets of rules. Gentzen-style systems have significant practical and theoretical advantages compared to Hilbert-style systems. For example, both natural deduction and sequent calculus systems facilitate the elimination and introduction of universal and existential quantifiers so that unquantified logical expressions can be manipulated according to the much simpler rules of propositional calculus. In a typical argument, quantifiers are eliminated, then propositional calculus is applied to unquantified expressions (which typically contain free variables), and then the quantifiers are reintroduced. This very much parallels the way in which mathematical proofs are carried out in practice by mathematicians. Predicate calculus proofs are generally much easier to discover with this approach, and are often shorter. Natural deduction systems are more suited to practical theorem-proving. Sequent calculus systems are more suited to theoretical analysis. (Wikipedia).
Pre-Calculus - The vocabulary of linear functions and equations
This video will introduce you to a few of the terms that are commonly used with linear functions and equations. Pay close attention to how you can tell the difference between linear and non-linear functions. For more videos please visit http://www.mysecretmathtutor.com
From playlist Pre-Calculus
Calculus 1 Lecture 3.1: Increasing/Decreasing and Concavity of Functions
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From playlist Calculus 1 (Full Length Videos)
12_1_1 Introduction to Taylor Polynomials
An introduction to expand a function into a Taylor polynomial.
From playlist Advanced Calculus / Multivariable Calculus
Graham Leigh: On the computational content of classical sequent calculus
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Computational interpretations of classical logic are entwined with constructive proofs of Herbrand's Theorem which states, its simplest form, that for every valid existen
From playlist Workshop: "Proofs and Computation"
A Brief Tour of Proof Complexity: Lower Bounds and Open Problems - Toniann Pitassi
Computer Science/Discrete Mathematics Seminar II Topic: A Brief Tour of Proof Complexity: Lower Bounds and Open Problems Speaker: Toniann Pitassi Affiliation: University of Toronto; Visiting Professor, School of Mathematics Date: March 19, 2019 For more video please visit http://video.ia
From playlist Mathematics
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From playlist Engineering
In this video, we investigate how to compute limits of a function that is given graphically.
From playlist Calculus
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From playlist Calculus 1 (Full Length Videos)
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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Concavity and Parametric Equations Example. We find the open t-intervals on which the graph of the parametric equations is concave upward and concave downward.
From playlist Calculus
Sam Buss: Expanders in VNC^1 and Monotone Propositional Proofs
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: We give a combinatorial analysis of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson [2002], and show that this analysis can be fo
From playlist Workshop: "Proofs and Computation"
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Linear logic is a refinement of intuitionistic logic which, viewed as a functional programming language in the sense of the Curry-Howard correspondence, has an explicit mechanism for copying and discarding information. It turns out that, due to these mechanisms, linear logic is naturally r
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Calculus 9.3 Separable Equations
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
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Now we expand the creation of a Taylor Polynomial to multivariable functions.
From playlist Advanced Calculus / Multivariable Calculus
ConMed: Linvatec™ Sequent Meniscal Repair
Learn more about Nucleus for pharmaceuticals and medical devices: http://www.nucleusmedicalmedia.com/?utm_source=youtube&utm_medium=video-description&utm_campaign=conmed-101911 This custom 3D animation depicts knee preservation, and shows the Meniscal Repair Surgical Technique using the
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Linear differential equations: how to solve
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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
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Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in
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The Computer Chronicles - Parallel Processing (1986)
Special thanks to archive.org for hosting these episodes. Downloads of all these episodes and more can be found at: http://archive.org/details/computerchronicles
From playlist The Computer Chronicles 1986 Episodes
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