Formal languages | Logic symbols
In logic, the formal languages used to create expressions consist of symbols, which can be broadly divided into constants and variables. The constants of a language can further be divided into logical symbols and non-logical symbols (sometimes also called logical and non-logical constants). The non-logical symbols of a language of first-order logic consist of predicates and individual constants. These include symbols that, in an interpretation, may stand for individual constants, variables, functions, or predicates. A language of first-order logic is a formal language over the alphabet consisting of its non-logical symbols and its logical symbols. The latter include logical connectives, quantifiers, and variables that stand for statements. A non-logical symbol only has meaning or semantic content when one is assigned to it by means of an interpretation. Consequently, a sentence containing a non-logical symbol lacks meaning except under an interpretation, so a sentence is said to be true or false under an interpretation. These concepts are defined and discussed in the article on first-order logic, and in particular the section on syntax. The logical constants, by contrast, have the same meaning in all interpretations. They include the symbols for truth-functional connectives (such as "and", "or", "not", "implies", and logical equivalence) and the symbols for the quantifiers "for all" and "there exists". The equality symbol is sometimes treated as a non-logical symbol and sometimes treated as a symbol of logic. If it is treated as a logical symbol, then any interpretation will be required to interpret the equality sign using true equality; if interpreted as a non-logical symbol, it may be interpreted by an arbitrary equivalence relation. (Wikipedia).
Truth Tables for Compound Statements
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From playlist Logic (If-Then Statements, Truth Tables)
Simplify Statements Using Logically Equivalent Statements
This video explains how to simplify given statements using logically equivalent statements. mathspower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Determining the negation of a hypothesis and conclusion from a statement
👉 Learn how to find the negation of a statement. The negation of a statement is the opposite of the statement. It is the 'not' of a statement. If a statement is represented by p, then the negation is represented by ~p. For example, The statement "It is raining" has a negation of "It is not
From playlist Negation of a Statement
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
Introduction to Logically Equivalent Statements
This video introduces logically equivalent statements and defines De Morgan's laws, implications are disjunctions, double negation, and negation of an implication. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Understanding Logical Statements 3
U12_L1_T2_we3 Understanding Logical Statements 3
From playlist Algebra I Worked Examples
What is the negation of a statement and examples
👉 Learn how to find the negation of a statement. The negation of a statement is the opposite of the statement. It is the 'not' of a statement. If a statement is represented by p, then the negation is represented by ~p. For example, The statement "It is raining" has a negation of "It is not
From playlist Negation of a Statement
The True Power of Model Theory – Compactness, Infinitesimals and Ax's theorem
Thanks for watching! Go check out all submissions to 3blue1brown's contest: https://3b1b.co/SoME1 Corrections and remarks: none yet, let me know in the comments if you have any. Sources and resources: – First-order logic, compactness theorem David Marker's book: https://www.springer.com
From playlist Summer of Math Exposition Youtube Videos
End-to-End Differentiable Proving: Tim Rocktäschel, University of Oxford
We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specific
From playlist Logic and learning workshop
mod-26 lec-27 Basic Devices, Symbols and Circuits
Fundamentals of Industrial Oil Hydraulics and Pneumatics by Prof. R.N. Maiti,Department of Mechanical Engineering,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Fundamentals of Industrial Oil Hydraulics and Pneumatics (CosmoLearning Mechanical Engineering)
Logic 3 - Propositional Logic Semantics | 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
Gabriele Giannantoni explains the logic of Aristotle in the context of the history of logic in interview from 1990. These clips are from the Multimedia Encyclopedia of the Philosophical Sciences. The translation is my own. #Philosophy #Aristotle
From playlist Aristotle
Foundations S2 - Seminar 8 - Light discussion of soundness, completeness, first vs second order
A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. In this seminar Billy leads a discussion of soundness, completeness and first vs second-order logic, as a recap of some of what has been discussed over the past few months in the seminar. The webpage f
From playlist Foundations seminar
Truth Tables for Conditional Statements
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From playlist Logic (If-Then Statements, Truth Tables)
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Proved Cook-Levin Theorem: SAT is NP-c
From playlist MIT 18.404J Theory of Computation, Fall 2020
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)
Foundations S2 - Seminar 7 - Nonstandard models of arithmetic
A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. In this lecture Billy uses ultrafilters to construct nonstandard models of arithmetic, the hypernaturals. Near the end is some discussion of how to read this as talking about the limits of first order l
From playlist Foundations seminar