Predicate logic | Quantifier (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier in the first order formula expresses that everything in the domain satisfies the property denoted by . On the other hand, the existential quantifier in the formula expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable. The mostly commonly used quantifiers are and . These quantifiers are standardly defined as duals; in classical logic, they are interdefinable using negation. They can also be used to define more complex quantifiers, as in the formula which expresses that nothing has the property . Other quantifiers are only definable within second order logic or higher order logics. Quantifiers have been generalized beginning with the work of Mostowski and Lindström. In a first-order logic statement, quantifications in the same type (either universal quantifications or existential quantifications) can be exchanged without changing the meaning of the statement, while the exchange of quantifications in different types changes the meaning. As an example, the only difference in the definition of uniform continuity and (ordinary) continuity is the order of quantifications. First order quantifiers approximate the meanings of some natural language quantifiers such as "some" and "all". However, many natural language quantifiers can only be analyzed in terms of generalized quantifiers. (Wikipedia).
Introduction to Predicates and Quantifiers
This lesson is an introduction to predicates and quantifiers.
From playlist Mathematical Statements (Discrete Math)
Discrete Math - 1.4.3 Negating and Translating with Quantifiers
Negating the Universal and Existential Quantifiers and De Morgan's Laws for Quantifiers. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
From playlist Discrete Math I (Entire Course)
Determine the Negation, Converse, and Contrapositive of a Quantifier Statement (Symbols)
This video explains how to find the negation, converse, and contrapositive of a quantifier statement using symbols. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Maths for Programmers: Logic (Logical Quantifiers)
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From playlist Maths for Programmers
Universal and Existential Quantifiers, ∀ "For All" and ∃ "There Exists"
Statements with "for all" and "there exist" in them are called quantified statements. "For all", written with the symbol ∀, is called the Universal Quantifier and and "There Exists" , written with the symbol ∃, is called the Existential Quantifier. A quantifier turns a predicate such as "x
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Simplify the Negation of Statements with Quantifiers and Predicates
This video provides two examples of how to determine simplified logically equivalent statements containing quantifiers and predicates. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Predicate and Quantifier Concept Check 1
This example provides a concept check for the understanding of quantifiers and quantified statements.
From playlist Mathematical Statements (Discrete Math)
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Predicates and Quantifiers [Discrete Math Class]
This video is not like my normal uploads. This is a supplemental video from one of my courses that I made in case students had to quarantine. This is a follow up to previous videos introducing propositional logic (mathematical propositions; logical connectives - "and", "or", "not" , the co
From playlist Discrete Mathematics Course
This E-Lecture builds upon Predicate Logic I and discusses the main principles of quantification. Prof. Handke explains how to use and interpret the universal, the existential and the negative quantifier and uses several examples for illustration.
From playlist VLC103 - The Nature of Meaning
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
Logic 7 - First Order Logic | Stanford CS221: AI (Autumn 2021)
For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai Associate Professor Percy Liang Associate Professor of Computer Science and Statistics (courtesy) https://profiles.stanford.edu/percy-liang Assistant Professor
From playlist Stanford CS221: Artificial Intelligence: Principles and Techniques | Autumn 2021
Pascal Fontaine - SMT: quantifiers, and future prospects - IPAM at UCLA
Recorded 16 February 2023. Pascal Fontaine of the Université de Liège presents "SMT: quantifiers, and future prospects" at IPAM's Machine Assisted Proofs Workshop. Abstract: Satisfiability Modulo Theory (SMT) is a paradigm of automated reasoning to tackle problems related to formulas conta
From playlist 2023 Machine Assisted Proofs Workshop
"What are you actually talking about?" Quantifiers help us specify our domain of discourse (the things we're talking about) so that our mathematical writing produces statements instead of, um, confusions.
From playlist Linear Algebra
PREDICATE LOGIC and QUANTIFIER NEGATION - DISCRETE MATHEMATICS
Today we wrap up our discussion of logic by introduction quantificational logic. This includes talking about existence and universality. We also discuss the negation of our quantificational operators. Visit my website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--
From playlist Discrete Math 1
SCOPE and FREE and BOUND Variables in Predicate Logic - Logic
In this video on Logic, we learn how to identify scope as well as determine whether variables are free or bound. We also talk about whether a formula is open or closed. 0:00 - [Intro] 0:56 - [Scope] 4:22 - [Free and Bound Variables] 8:14 - [Open and Closed Formulas] 11:37 - [Exercise] #S
From playlist Logic in Philosophy and Mathematics