Five Kinds of Nondeterminism
(buttondown.com)
No newsletter next week, I'm teaching a TLA+ workshop.
No newsletter next week, I'm teaching a TLA+ workshop.
XOR
(greenend.org.uk)
Recently I was called on to explain the ‘XOR’ operator to somebody who vaguely knew of its existence, but didn’t have a good intuition for what it was useful for and how it behaved.
Recently I was called on to explain the ‘XOR’ operator to somebody who vaguely knew of its existence, but didn’t have a good intuition for what it was useful for and how it behaved.
Gödel's Loophole
(wikipedia.org)
Gödel's Loophole is a supposed "inner contradiction" in the Constitution of the United States which Austrian-American logician, mathematician, and analytic philosopher Kurt Gödel postulated in 1947.
Gödel's Loophole is a supposed "inner contradiction" in the Constitution of the United States which Austrian-American logician, mathematician, and analytic philosopher Kurt Gödel postulated in 1947.
Sequent Calculus and Notation – Par Part 1
(ryanbrewer.dev)
This post is the first in a series on Logic. These ideas are very useful in understanding many important papers on programming language theory, especially papers on type theory and the lambda calculus. I will start with an explanation of sequents and Sequent Calculus as a system for doing logic, then I'll dive into linear logic in the next post. I'll finish the trilogy with a post on Par and computational interpretations of classical logic.
This post is the first in a series on Logic. These ideas are very useful in understanding many important papers on programming language theory, especially papers on type theory and the lambda calculus. I will start with an explanation of sequents and Sequent Calculus as a system for doing logic, then I'll dive into linear logic in the next post. I'll finish the trilogy with a post on Par and computational interpretations of classical logic.
Who Can Understand the Proof? A Window on Formalized Mathematics
(stephenwolfram.com)
For more than a century people had wondered how simple the axioms of logic (Boolean algebra) could be. On January 29, 2000, I found the answer—and made the surprising discovery that they could be about twice as simple as anyone knew. (I also showed that what I found was the simplest possible.)
For more than a century people had wondered how simple the axioms of logic (Boolean algebra) could be. On January 29, 2000, I found the answer—and made the surprising discovery that they could be about twice as simple as anyone knew. (I also showed that what I found was the simplest possible.)
SAT Solver Etudes I
(philipzucker.com)
SAT solving is kind of too big a topic for one post. Here is some discussion, programs and links.
SAT solving is kind of too big a topic for one post. Here is some discussion, programs and links.
Lean: Programming Language and Theorem Prover
(lean-lang.org)
Programming Language and Theorem Prover
Programming Language and Theorem Prover
Transcendental Syntax
(github.com/engboris)
The transcendental syntax is a method of constructing logical abstractions from a low-level elementary and "logic-agnostic" language.
The transcendental syntax is a method of constructing logical abstractions from a low-level elementary and "logic-agnostic" language.
The Hoare Cube
(wordpress.com)
I wrote earlier this year about my attempt to understand the repercussions of toggling and when giving a semantics to Hoare triples.
I wrote earlier this year about my attempt to understand the repercussions of toggling and when giving a semantics to Hoare triples.
Beauty of the Gentzen System
(wyounas.github.io)
Gentzen system, created by German mathematician Gerhard Gentzen, is a deductive system which can be used to prove propositional formulas. I recently learned about it while I was reading Ben-Ari’s fantastic book on mathematical logic [1] and I like its simplicity.
Gentzen system, created by German mathematician Gerhard Gentzen, is a deductive system which can be used to prove propositional formulas. I recently learned about it while I was reading Ben-Ari’s fantastic book on mathematical logic [1] and I like its simplicity.
A boy girl paradox – or maybe not?
(shankwiler.com)
The most liked comment answers 1/2, but the user got worn down by others until he recanted and agreed that the answer is 1/3. Many other comments give lengthy explanations as to why the answer is 1/3.
The most liked comment answers 1/2, but the user got worn down by others until he recanted and agreed that the answer is 1/3. Many other comments give lengthy explanations as to why the answer is 1/3.
Question Sets and All Paths
(andrewpwheeler.com)
I was nerd-sniped with a question at work the other day. The set up was like this, imagine a survey where all of the questions have yes-no answers. Some of the answers are terminating, so if you answer No to a particular question, the questions stop. But some if you reach that part of the tree will keep going.
I was nerd-sniped with a question at work the other day. The set up was like this, imagine a survey where all of the questions have yes-no answers. Some of the answers are terminating, so if you answer No to a particular question, the questions stop. But some if you reach that part of the tree will keep going.
Category Theory Illustrated: Logic (2021)
(abuseofnotation.github.io)
Logic is the science of the possible. As such, it is at the root of all other sciences, all of which are sciences of the actual, i.e. that which really exists.
Logic is the science of the possible. As such, it is at the root of all other sciences, all of which are sciences of the actual, i.e. that which really exists.
The logical fallacy at the core of patent law, what does non-obviousness test?
(academic.oup.com)
Patent laws in different jurisdictions have in their core a logical fallacy that generations of patent professionals have kept practising while seemingly being oblivious to its existence.
Patent laws in different jurisdictions have in their core a logical fallacy that generations of patent professionals have kept practising while seemingly being oblivious to its existence.
LLMs can't perform "genuine logical reasoning," Apple researchers suggest
(arstechnica.com)
Irrelevant red herrings lead to "catastrophic" failure of logical inference.
Irrelevant red herrings lead to "catastrophic" failure of logical inference.
The box problem that baffled the boffins
(theguardian.com)
Earlier today I set you the following puzzle, which has been doing the rounds in the academic community, because of its counter-intuitive result. Here it is again with the solution.
Earlier today I set you the following puzzle, which has been doing the rounds in the academic community, because of its counter-intuitive result. Here it is again with the solution.
Mathiness
(votito.com)
Mathiness is a term for calculations and formulas that may look and feel like rigorous mathematics but lack true analytical rigor or validity, and often disregard logical coherence or factual accuracy.
Mathiness is a term for calculations and formulas that may look and feel like rigorous mathematics but lack true analytical rigor or validity, and often disregard logical coherence or factual accuracy.
Nirvana fallacy (Perfect solution fallacy)
(wikipedia.org)
The nirvana fallacy is the informal fallacy of comparing actual things with unrealistic, idealized alternatives.
The nirvana fallacy is the informal fallacy of comparing actual things with unrealistic, idealized alternatives.