Predicate logic | Systems of formal logic
In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order logic. The term "higher-order logic", abbreviated as HOL, is commonly used to mean higher-order simple predicate logic. Here "simple" indicates that the underlying type theory is the theory of simple types, also called the simple theory of types (see Type theory). Leon Chwistek and Frank P. Ramsey proposed this as a simplification of the complicated and clumsy ramified theory of types specified in the Principia Mathematica by Alfred North Whitehead and Bertrand Russell. Simple types is nowadays sometimes also meant to exclude polymorphic and dependent types. (Wikipedia).
Ex 1: Determine Higher Order Derivatives
This video provides an example of how to determine the first, second, third, and fourth derivative of a function. Complete Video List at http://www.mathispower4u.com
From playlist Higher Order Differentiation
Higher Order Derivatives of Trigonometric Functions
The video explains how to determine higher order derivatives of trigonometric functions. http://mathispower4u.wordpress.com/
From playlist Differentiation
11_8_1 Higher Order Partial Derivatives Part 1
Just as there are second, third, and higher-order derivatives in single variable calculus, so there are higher-order partial derivatives in multivariable calculus. the only differences being that these are partial derivatives and the can be combined in certain orders.
From playlist Advanced Calculus / Multivariable Calculus
C34 Expanding this method to higher order linear differential equations
I this video I expand the method of the variation of parameters to higher-order (higher than two), linear ODE's.
From playlist Differential Equations
(2.3.1) Introduction to Higher Order Linear Differential Equations and Related Theorem
The video introduces higher order linear differential equations and related theorems on superposition, existence and uniqueness, and linear independence. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Higher-Order Derivatives: Part 1 of 2
http://mathispower4u.wordpress.com/
From playlist Higher Order Differentiation
Ex 2: Determine Higher Order Derivatives
This video provides an example of how to determine the first, second, and third derivative of a function. Complete Video List at http://www.mathispower4u.com
From playlist Higher Order Differentiation
B14 Simplifying a system of higher order ODEs
Simplifying a system of higher-order ODE's in order to solve them through numerical analysis.
From playlist A Second Course in Differential Equations
Types Of Differential Equations
Introduction to the Order of a differential equation and the idea of Linear and Non-linear differential equations. Discussion of how the number of constants of a general solution is related to the order of a differential equation.
From playlist Mathematical Physics I Uploads
Constructive Type Theory and Homotopy - Steve Awodey
Steve Awodey Institute for Advanced Study December 3, 2010 In recent research it has become clear that there are fascinating connections between constructive mathematics, especially as formulated in the type theory of Martin-Löf, and homotopy theory, especially in the modern treatment in
From playlist Mathematics
Live CEOing Ep 263: Predicate Logic Theorem Proving in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Predicate Logic Theorem Proving in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
This computer science video follows on from the video about combining logic gates. It covers how a logic gate diagram can be described with a Boolean expression. This includes how to come up with a valid expression for a given combination of logic gates and, conversely, how to draw a log
From playlist Logic Gates
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
Logic 1 - Overview: Logic Based Models | Stanford CS221: AI (Autumn 2021)
For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai This lecture covers logic-based models: propositional logic, first order logic Applications: theorem proving, verification, reasoning, think in terms of logical f
From playlist Stanford CS221: Artificial Intelligence: Principles and Techniques | Autumn 2021
Lecture 1: Invitation to topos theory
This talk introduces the motivating question for this semester of the Curry-Howard seminar, which is how to organise mathematical knowledge using topoi. The approach sketched out in the talk is via first-order theories, their associated classifying topoi, and adjoint pairs of functors betw
From playlist Topos theory seminar
Semantic models for higher-order Bayesian inference - Sam Staton, University of Oxford
In this talk I will discuss probabilistic programming as a method of Bayesian modelling and inference, with a focus on fully featured probabilistic programming languages with higher order functions, soft constraints, and continuous distributions. These languages are pushing the limits of e
From playlist Logic and learning workshop
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Mathematical Aspects of Computer Science
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
High-Order Ordinary Differential Equations with More Derivatives (from Physics)
Here we show how to derive higher-order differential equation systems, with higher-order derivatives, from F=ma by chaining together simple systems. Our example is combining two spring-mass systems to get a fourth order equation. Playlist: https://www.youtube.com/playlist?list=PLMrJAk
From playlist Engineering Math: Differential Equations and Dynamical Systems