Propositional calculus | Rules of inference | Inference | Formal systems | Logical expressions

Rule of inference

In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics), in the sense that if the premises are true (under an interpretation), then so is the conclusion. Typically, a rule of inference preserves truth, a semantic property. In many-valued logic, it preserves a general designation. But a rule of inference's action is purely syntactic, and does not need to preserve any semantic property: any function from sets of formulae to formulae counts as a rule of inference. Usually only rules that are recursive are important; i.e. rules such that there is an effective procedure for determining whether any given formula is the conclusion of a given set of formulae according to the rule. An example of a rule that is not effective in this sense is the infinitary ω-rule. Popular rules of inference in propositional logic include modus ponens, modus tollens, and contraposition. First-order predicate logic uses rules of inference to deal with logical quantifiers. (Wikipedia).

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Causal Inference Introduction

Causal Inference is a set of tools used to scientifically prove cause and effect, very commonly used in economics and medicine. This series will go over the basics that any data scientist should understand about causal inference - and point them to the tools they would need to perform it.

From playlist Causal Inference - The Science of Cause and Effect

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Ideal Experiment - Causal Inference

In this video, I give you more details about the fundamental question and the fundamental problem of causal inference with the help of an example (our ideal experiment).

From playlist Causal Inference - The Science of Cause and Effect

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Discrete Math - 1.6.1 Rules of Inference for Propositional Logic

Building a valid argument using rules of inference for propositions. 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)

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RULES of INFERENCE - DISCRETE MATHEMATICS

We talk about rules of inference and what makes a valid argument. We discuss modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, addition, simplification, and conjunction. #DiscreteMath #Mathematics #Logic #RulesOfInference LIKE AND SHARE THE VIDEO IF IT HELPED!

From playlist Discrete Math 1

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t Test Write Up of a Hypothesis Test of an Unknown Population Mean

How to perform and write up a hypothesis test [t test] of an unknown population mean [In accordance with AP Statistics requirements]

From playlist Unit 9: t Inference and 2-Sample Inference

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Assumptions - Causal Inference

In this video, I introduce the most important assumptions in casual inference that we use in order to avoid mistakes such as presuming association and causation to be one and the same, among others: - Positivity - SUTVA - Large Sample Size - Double Blinded - No Measurement Error - Exchan

From playlist Causal Inference - The Science of Cause and Effect

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Fundamental Question - Causal Inference

In this video, I define the fundamental question and problem of causal inference and use an example to further explain the concept.

From playlist Causal Inference - The Science of Cause and Effect

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2 Sample t Test v Paired t Test

Identifying the difference between situations when a 2-sample t Test is appropriate and when a paired t Test is appropriate, including the recognition of paired dependent data versus independent samples.

From playlist Unit 9: t Inference and 2-Sample Inference

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Logic 4 - Inference Rules | 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

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Brief Introduction to Statistical Inference - Causal Inference

In this video, I briefly introduce the topic of Statistical Inference and go over its most fundamental concepts - those that we will use in this series. If you want to learn more about this stuff, check out this link to my entire series on Statistical Inference: https://www.youtube.com/pla

From playlist Causal Inference - The Science of Cause and Effect

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Foundations - Seminar 2

Billy Price and Will Troiani present a series of seminars on foundations of mathematics. In this seminar Billy introduces natural deduction as a proof system. You can join this seminar from anywhere, on any device, at https://www.metauni.org. This video was filmed in Deprecation (https:/

From playlist Foundations seminar

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How to create a fuzzy inference system

Learn how to graphically design and simulate fuzzy inference systems using the fuzzy logic designer app. The video demonstrates the steps to create a fuzzy logic to estimate the tip percentage for a waiter based on the quality of food and service. - Build fuzzy inference systems and fuzz

From playlist “How To” with MATLAB and Simulink

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Logic 1 - Propositional Logic | Stanford CS221: AI (Autumn 2019)

For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3ChWesU Topics: Logic Percy Liang, Associate Professor & Dorsa Sadigh, Assistant Professor - Stanford University http://onlinehub.stanford.edu/ Associate Professor

From playlist Stanford CS221: Artificial Intelligence: Principles and Techniques | Autumn 2019

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Formal Logic

This video functions as a brief introduction to many different topics in formal logic. Notes on the Images: I looked into the legality of using images for this video a good deal and I've come to the conclusion that there is nothing in this video which could remotely imply these images ar

From playlist Summer of Math Exposition 2 videos

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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

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Logic 10 - Recap | Stanford CS221: Artificial Intelligence (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

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Geoffrey Hinton: "Introduction to Deep Learning & Deep Belief Nets"

Graduate Summer School 2012: Deep Learning, Feature Learning "Part 1: Introduction to Deep Learning & Deep Belief Nets" Geoffrey Hinton, University of Toronto Institute for Pure and Applied Mathematics, UCLA July 9, 2012 For more information: https://www.ipam.ucla.edu/programs/summer-sc

From playlist GSS2012: Deep Learning, Feature Learning

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Inference Rules via the Algebra of Boole | MathFoundations 275 | N J Wildberger

We show how to introduce Inference Rules in Propositional Logic in the framework of the Algebra of Boole, which provides a cut and dried technology to easily establish all such rules. Prominent amongst these are Modus Ponens, Modus Tollens, Hypothetical Syllogism and Disjunctive Syllogism

From playlist Boole's Logic and Circuit Analysis

Related pages

Natural deduction | Syntax (logic) | List of rules of inference | Infinite set | Theorem | Contraposition | Hilbert system | Modus tollens | Logical truth | Structural rule | Sequent calculus | Sequent | Non-classical logic | Many-valued logic | Natural number | Law of thought | Lewis Carroll | Proposition | Metavariable | Mathematical induction | Modus ponens | Deduction theorem | Three-valued logic | Ω-consistent theory | Logical connective | Philosophy of logic | Immediate inference | Classical logic | Deductive reasoning | Recursion