Hacker News with Generative AI: 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.)

Mathematics, Logic, Boolean Algebra, Research, History

188 points by ColinWright 8 days ago | 115 comments

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 Solvers, Programming, Logic, Computer Science

45 points by mathgenius 11 days ago | 30 comments

Lean: Programming Language and Theorem Prover (lean-lang.org)
Programming Language and Theorem Prover

Programming Languages, Theorem Provers, Logic

9 points by SerCe 14 days ago | 0 comments

Transcendental Syntax (github.com/engboris)
The transcendental syntax is a method of constructing logical abstractions from a low-level elementary and "logic-agnostic" language.

Programming, Software, Logic, Computer Science

81 points by 4ad 14 days ago | 34 comments

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.

Programming, Logic, Computer Science, Formal Verification

86 points by matt_d 44 days ago | 23 comments

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.

Mathematics, Logic, Proof Systems

6 points by simplegeek 45 days ago | 0 comments

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.

Probability, Math, Puzzles, Logic

12 points by iuvcaw 62 days ago | 0 comments

The Laws of Thought by George Boole (1854) (gutenberg.org)

Logic, History, Mathematics, Books

8 points by sandwichsphinx 66 days ago | 0 comments

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.

Algorithms, Logic, Programming

5 points by apwheele 77 days ago | 5 comments

Algorithm = Logic and Control [pdf] (ic.ac.uk)

Algorithm, Computer Science, Logic, Control

72 points by acmerfight 79 days ago | 12 comments

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.

Category Theory, Mathematics, Logic

252 points by boris_m 85 days ago | 83 comments

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.

Law, Logic, Patents

12 points by croes 92 days ago | 21 comments

LLMs can't perform "genuine logical reasoning," Apple researchers suggest (arstechnica.com)
Irrelevant red herrings lead to "catastrophic" failure of logical inference.

Artificial Intelligence, Logic, Research

115 points by samizdis 95 days ago | 73 comments

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.

Puzzles, Math, Logic

11 points by sorokod 109 days ago | 12 comments

How can a jigsaw have two distinct solutions? [video] (youtube.com)

Puzzles, Mathematics, Video, Logic

80 points by patrakov 111 days ago | 31 comments

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.

Mathematics, Logic, Science, Misinformation

89 points by adzicg 113 days ago | 52 comments

Nirvana fallacy (Perfect solution fallacy) (wikipedia.org)
The nirvana fallacy is the informal fallacy of comparing actual things with unrealistic, idealized alternatives.

Logic, Fallacies, Critical Thinking

12 points by yamrzou 121 days ago | 4 comments

Kids Should Be Taught to Think Logically (scientificamerican.com)

Education, Logic, Children

44 points by LinuxBender 135 days ago | 76 comments

Category Theory (logicmatters.net)

Mathematics, Logic, Computer Science

17 points by Schiphol 142 days ago | 2 comments

Can mathematical definitions of form "P if Q" mean "P if and only if Q"? (2012) (stackexchange.com)

Mathematics, Logic, Definitions, Mathematical Notation

7 points by susam 154 days ago | 5 comments

The Politician's Syllogism (wikipedia.org)