Mathematical logic | Modal logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators and , representing possibility and necessity respectively. For instance the modal formula can be read as "possibly " while can be read as "necessarily ". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When is used to represent epistemic necessity, states that is epistemically necessary, or in other words that it is known. When is used to represent deontic necessity, states that is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a possible world. A formula's truth value at one possible world can depend on the truth values of other formulas at other accessible possible worlds. In particular, is true at a world if is true at some accessible possible world, while is true at a world if is true at every accessible possible world. A variety of proof systems exist which are sound and complete with respect to the semantics one gets by restricting the accessibility relation. For instance, the deontic modal logic D is sound and complete if one requires the accessibility relation to be serial. While the intuition behind modal logic dates back to antiquity, the first modal axiomatic systems were developed by C. I. Lewis in 1912. The now-standard relational semantics emerged in the mid twentieth century from work by Arthur Prior, Jaakko Hintikka, and Saul Kripke. Recent developments include alternative topological semantics such as neighborhood semantics as well as applications of the relational semantics beyond its original philosophical motivation. Such applications include game theory, moral and legal theory, web design, multiverse-based set theory, and social epistemology. (Wikipedia).
Modal logic formalization of chess
In this video I explain modal logic using the example of the legal configurations of a board game. Kripke semantic and Kripke frames are discussed. The relation to Temporal and Doxastic logics are motivated. Here's the formal logic text from the video: https://gist.github.com/Nikolaj-K/174
From playlist Logic
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
What are Non-Classical logics?
Some of the general classes of non-classical logics I touch in this videos are linear logic, relevant logic, modal logic, many-valued logics, minimal logic, paraconsistent logics and so on and so forth. Let me know if I should dive deeping into a certain scene? https://en.wikipedia.org/wi
From playlist Programming
Bas Spitters: Modal Dependent Type Theory and the Cubical Model
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: In recent years we have seen several new models of dependent type theory extended with some form of modal necessity operator, including nominal type theory, guarded and c
From playlist Workshop: "Types, Homotopy, Type theory, and Verification"
Logic for Programmers: Propositional Logic
Logic is the foundation of all computer programming. In this video you will learn about propositional logic. 🔗Homework: http://www.codingcommanders.com/logic.php 🎥Logic for Programmers Playlist: https://www.youtube.com/playlist?list=PLWKjhJtqVAbmqk3-E3MPFVoWMufdbR4qW 🔗Check out the Cod
From playlist Logic for Programmers
Introduction to Predicate Logic
This video introduces predicate logic. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Damiano Mazza: Heterodox exponential modalities in linear logic
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: Quantifiers (univ. & exist.), Proofs part 1 — Tutorial 3/4
In this four-part series we explore propositional logic, Karnaugh maps, implications and fallacies, predicate logic, existential and universal quantifiers and finally natural deduction. Become a member: https://youtube.com/Bisqwit/join My links: Twitter: https://twitter.com/RealBisqwit L
From playlist Logic Tutorial
Avicenna on Existence (History of Philosophy)
Peter Adamson discusses Avicenna and how he revolutionized metaphysics with groundbreaking ideas about necessity and contingency, and his new distinction between essence and existence. This is an episode of Peter Adamson's podcast on the History of Philosophy from a few years back. For mor
From playlist Shorter Clips & Videos - Philosophy Overdose
Linguistically informed NLP for healthcare experience data | Healthcare NLP Summit 2021
Get your Free Spark NLP and Spark OCR Free Trial: https://www.johnsnowlabs.com/spark-nlp-try-free/ Register for NLP Summit 2021: https://www.nlpsummit.org/2021-events/ Watch all Healthcare NLP Summit 2021 sessions: https://www.nlpsummit.org/ Investigation of attention mechanisms of BER
From playlist Healthcare NLP Summit 2021
On the Category of hSets - Bas Spitters
On the Category of hSets - Bas Spitters Bas Spitters Radboud University Nijmegen; Member, School of Mathematics April 3, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
How to Work Out ALL of the Averages from Frequency Tables | Grade 5 Series | GCSE Maths Tutor
A video revising the techniques and strategies for completing averages from frequency tables. (Higher & Foundation). This video is part of the Statistics module in GCSE maths, see my other videos below to continue with the series. These are the calculators that I recommend 💎 Casio fx-8
From playlist GCSE Maths Videos
This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.
From playlist Linear algebra: theory and implementation
Proof synthesis and differential linear logic
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
From playlist Talks
On Voevodsky's univalence principle - André Joyal
Vladimir Voevodsky Memorial Conference Topic: On Voevodsky's univalence principle Speaker: André Joyal Affiliation: Université du Québec á Montréal Date: September 11, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics