Formal languages | Model theory
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation. In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language. For example, an interpretation function could take the predicate T (for "tall") and assign it the extension {a} (for "Abraham Lincoln"). Note that all our interpretation does is assign the extension {a} to the non-logical constant T, and does not make a claim about whether T is to stand for tall and 'a' for Abraham Lincoln. Nor does logical interpretation have anything to say about logical connectives like 'and', 'or' and 'not'. Though we may take these symbols to stand for certain things or concepts, this is not determined by the interpretation function. An interpretation often (but not always) provides a way to determine the truth values of sentences in a language. If a given interpretation assigns the value True to a sentence or theory, the interpretation is called a model of that sentence or theory. (Wikipedia).
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
This video teaches students how to write the inverse of a conditional statement. In particular, this video goes into detail about how to negate the hypothesis and conclusion of a conditional statement. In addition, the concepts of truth value, negating statements and logical equivalence ar
From playlist Geometry
This video focuses on how to write the converse of a conditional statement. In particular, this video shows how to flip the hypothesis and conclusion of a conditional statement. The concepts of truth value and logical equivalence are explored as well. Your feedback and requests are encour
From playlist Geometry
An introduction to the general types of logic statements
From playlist Geometry
Defining and comprehending "implication" in Mathematics
I'm not a native English speaker, sorry about my pronunciation and fluency in English. If there is any kind of mistake in the video, please inform me in the comments section.
From playlist Summer of Math Exposition Youtube Videos
Scope Ambiguity - Semantics in Linguistics
We take a look at Scope Ambiguity in this #semantics and #syntax video in #linguistics. We look at logical form to see how we can represent this in a tree structure to get two meanings. We also look at a little trick of translating predicate logic sentences with more than one quantifier.
From playlist Semantics in Linguistics
Learning to write the inverse of a conditional statement
👉 Learn how to find the inverse of a statement. The inverse of a statement is the negation of the hypothesis and the conclusion of a conditional statement. If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the conditional statement is represe
From playlist Inverse of a Statement
What are examples of a statements converse, inverse, and contrapositive
👉 Learn how to find the inverse, the converse, and the contrapositive of a statement. The contrapositive of a statement is the switching of the hypothesis and the conclusion of a conditional statement and negating both. If the hypothesis of a statement is represented by p and the conclusio
From playlist Converse, Inverse, Contrapositive Conditional Statements
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
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
Quantum Physics – list of Philosophical Interpretations
Explanation of the various interpretations of Quantum Mechanics. My Patreon page is at https://www.patreon.com/EugeneK 00:00 Introduction 00:29 Copenhagen Interpretation 02:08 Objective Collapse 04:41 EPR Paradox 06:11 Retro-Causality 07:28 Transactional Interpretation 10:25 Super-Determ
From playlist Physics
Marie Kerjean: Differential linear logic extended to differential operators
HYBRID EVENT Recorded during the meeting Linear Logic Winter School" the January 28, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual
From playlist Logic and Foundations
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
http://www.teachastronomy.com/ Logic is a fundamental tool of the scientific method. In logic we can combine statements that are made in words or in mathematical symbols to produce concrete and predictable results. Logic is one of the ways that science moves forward. The first ideas of
From playlist 01. Fundamentals of Science and Astronomy