Fixed points (mathematics) | Game theory

Common knowledge (logic)

Common knowledge is a special kind of knowledge for a group of agents. There is common knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum. It can be denoted as . The concept was first introduced in the philosophical literature by David Kellogg Lewis in his study Convention (1969). The sociologist Morris Friedell defined common knowledge in a 1969 paper. It was first given a mathematical formulation in a set-theoretical framework by Robert Aumann (1976). Computer scientists grew an interest in the subject of epistemic logic in general – and of common knowledge in particular – starting in the 1980s. There are numerous puzzles based upon the concept which have been extensively investigated by mathematicians such as John Conway. The philosopher Stephen Schiffer, in his 1972 book Meaning, independently developed a notion he called "mutual knowledge" which functions quite similarly to Lewis's and Friedel's 1969 "common knowledge". If a trustworthy announcement is made in public, then it becomes common knowledge; However, if it is transmitted to each agent in private, it becomes mutual knowledge but not common knowledge. Even if the fact that "every agent in the group knows p" is transmitted to each agent in private, it is still not common knowledge: . But, if any agent publicly announces their knowledge of p, then it becomes common knowledge that they know p (viz. ). If every agent publicly announces their knowledge of p, p becomes common knowledge . (Wikipedia).

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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

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Introduction to Common Mathematical Proof Methods

This video introduces the common methods of mathematical proofs and provides a basic example of a direct proof. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Teach Astronomy - Logic

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From playlist 01. Fundamentals of Science and Astronomy

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This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

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From playlist Logic (If-Then Statements, Truth Tables)

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From playlist Philosophy

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From playlist ISE Conference Talks

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Frege, Russell, & Modern Logic - A. J. Ayer & Bryan Magee (1987)

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From playlist Bryan Magee Interviews - The Great Philosophers (1987)

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Wilfrid Sellars (1966) Science & Ethics: A Study in First Principles

Sellars’s speech centers on natural and social sciences’ relationship to morality. In the context of conducting several thought experiments, Sellars explores what the act of valuation means to ethicists as opposed to scientists. This talk was given by Wilfrid Sellars in 1966 as part of t

From playlist Ethics & Moral Philosophy

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This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

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Keynote at 6th International Conference on Graphs and Networks in the Humanities 2022 Prof. Dr. Harald Sack FIZ Karlsruhe - Leibniz Institute for Informaation Infrastructure Karlsruhe Institute of Technology Slides: https://bit.ly/WithKnowledgeDoubtIncreases FIZ ISE on twitter: https:/

From playlist ISE Conference Talks

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What Are Numbers? Philosophy of Mathematics (Elucidations)

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From playlist Logic & Philosophy of Mathematics

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A World of Pure Experience (By William James)

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From playlist Philosophy of Mind

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Maths for Programmers: Logic (What Is Logic?)

We're busy people who learn to code, then practice by building projects for nonprofits. Learn Full-stack JavaScript, build a portfolio, and get great references with our open source community. Join our community at https://freecodecamp.com Follow us on twitter: https://twitter.com/freecod

From playlist Maths for Programmers

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Clojure Conj 2012 - Challenges for Logic Programming

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From playlist Clojure Conf 2012

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From playlist CISA Training Videos

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Julio Saez-Rodriguez: Networks of prior knowledge as frames to understand complex biological data

Modern technologies allow us to profile in high detail biomedical samples at fast decreasing costs. New technologies are opening new data modalities, in particular to measure at the single cell level. Prior knowledge, and biological networks in particular, are useful to integrate this data

From playlist Mathematics in Science & Technology

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What the World Gets Wrong about Science

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From playlist Science

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Knowledge - Lecture 1 - CS50's Introduction to Artificial Intelligence with Python 2020

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From playlist CS50's Introduction to Artificial Intelligence with Python 2020

Related pages

Multimodal logic | Logic puzzle | Set theory | Truth value | Econometrica | Mutual knowledge (logic) | John Horton Conway | Stag hunt | Global game | Prior probability | Transitive closure | Kripke semantics | Induction puzzles | Well-formed formula | Game theory | Ad infinitum | Dynamic epistemic logic | Partition of a set | Epistemic modal logic | Aumann's agreement theorem | Strategy (game theory) | Mutual knowledge | Reflexive closure | Nash equilibrium | Axiom | Agent-based model | Two Generals' Problem | Kripke structure (model checking)