Hacker News with Generative AI: Logic

Using Logic in Writing (owl.purdue.edu)
Understanding how to create logical syllogisms does not automatically mean that writers understand how to use logic to build an argument.

Writing, Logic, Argumentation

66 points by benjacksondev 32 days ago | 19 comments

Looking for Keys Under the Lamppost (johndcook.com)
There’s an old joke about a drunk man looking for his keys under a lamppost. Someone stops and offers to help. He asks, “So, did you lose your keys here?” The drunk replies “No, I lost them over there, but here’s where the light is.”

Humor, Logic, Problem Solving

10 points by zdw 33 days ago | 5 comments

A SomewhatMaxSAT Solver (jak-linux.org)
As you may recall from previous posts and elsewhere I have been busy writing a new solver for APT. Today I want to share some of the latest changes in how to approach solving.

Software, Programming, Logic, Optimization

9 points by JNRowe 34 days ago | 0 comments

Show HN: Formalizing Principia Mathematica using Lean (github.com/ndrwnaguib)
This project aims to formalize the first volume of Prof. Bertrand Russell’s Principia Mathematica using the Lean theorem prover.

Mathematics, Formal Verification, Theorem Proving, Logic

188 points by ndrwnaguib 63 days ago | 34 comments

Show HN: Logiquiz – Daily Self-Referential Puzzles (logiquiz.com)
Logiquiz, also know as Self-Referential Quiz or Puzzle, is a type of quiz where the questions refer to the quiz itself or other questions within the same quiz. The answers often depend on the content or structure of the quiz, making it a meta-puzzle.

Puzzles, Games, Self-Referential, Logic, Daily

38 points by slig 65 days ago | 20 comments

Surprises in Logic (2016) (math.ucr.edu)
There's a complexity barrier built into the very laws of logic: roughly speaking, while lots of things are more complex than this, we can't prove any specific thing is more complex than this. And this barrier is surprisingly low! Just how low? Read this.

Mathematics, Logic, Complexity

92 points by jxmorris12 66 days ago | 42 comments

Conspiracies Are Often Unnecessary (curi.us)
David Deutsch wrote an article about conspiracy theories and we had conversations about them. It's an interesting topic which is worth analyzing not just dismissing. I now think he was right about some of the logic of his analysis, but wrong about how it applies to the world. Deutsch says:

Conspiracy Theories, Logic, Analysis

5 points by speckx 73 days ago | 0 comments

PyReason: Explainable inference for annotated, real valued, graph based and tem (github.com/lab-v2)
PyReason is a graphical inference tool that uses a set of logical rules and facts (initial conditions) to reason over graph structures.

Graphical Inference, Logic, Python, Graph Structures

27 points by todsacerdoti 80 days ago | 2 comments

Novel Logic-Enhanced LLM for Improved Symbolic Reasoning (ycombinator.com)
I’m experimenting with a novel approach that integrates symbolic logic directly into a transformer’s attention mechanism.

Artificial Intelligence, Logic, Symbolic Reasoning

10 points by N3Xxus_6 84 days ago | 0 comments

Show HN: TypeScript as a proof assistant for intuitionistic propositional logic (github.com)
TypeScript can be used just like a proof assistant (for intuitionistic propositional logic)!

TypeScript, Proof Assistants, Logic, Programming Languages, Computer Science

17 points by xxmarijnw 88 days ago | 3 comments

Argumentation Theory (wikipedia.org)
Argumentation theory is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning.

Argumentation Theory, Logic, Philosophy, Linguistics

11 points by rnjailamba 96 days ago | 0 comments

Truth Functional Logic for Hackers (lagomor.ph)
Bob and Alice are two hackers working on an embedded system with a severe computational constraint - there is a bug in their low-cost microcontroller making OR operations significantly slower than any other operation on the chipset.

Logic, Programming, Hardware, Security

48 points by ChilledTonic 108 days ago | 14 comments

Translating natural language to first-order logic for logical fallacy detection (arxiv.org)
Translating natural language into formal language such as First-Order Logic (FOL) is a foundational challenge in NLP with wide-ranging applications in automated reasoning, misinformation tracking, and knowledge validation.

Logic, Artificial Intelligence, Automated Reasoning

258 points by ColinWright 115 days ago | 141 comments

Order Doesn’t Matter, But Reasoning Does (arxiv.org)

Artificial Intelligence, Reasoning, Logic

14 points by spaintech 116 days ago | 16 comments

Jan Łukasiewicz (wikipedia.org)
Jan Łukasiewicz (Polish: [ˈjan wukaˈɕɛvit͡ʂ] ⓘ; 21 December 1878 – 13 February 1956) was a Polish logician and philosopher who is best known for Polish notation and Łukasiewicz logic.[1] His work centred on philosophical logic, mathematical logic and history of logic.[2] He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle, offering one of the earliest systems of many-valued logic.

Logic, Philosophy, Poland, Biography, History

4 points by fuzztester 121 days ago | 1 comments

Five Kinds of Nondeterminism (buttondown.com)
No newsletter next week, I'm teaching a TLA+ workshop.

Computer Science, Programming, Theory, Logic, Formal Verification

135 points by BerislavLopac 128 days ago | 32 comments

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.

Logic, Programming, Computer Science, Binary Operations

602 points by mariuz 130 days ago | 100 comments

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.

Constitution, Philosophy, Logic, Mathematics

6 points by croes 137 days ago | 0 comments

Odds and Ends – Introductory Text on Probability and Inductive Logic [pdf] (jonathanweisberg.org)

Probability, Logic, Textbooks, Philosophy, Mathematics

8 points by rnjailamba 144 days ago | 0 comments

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.

Logic, Programming Languages, Type Theory, Lambda Calculus, Linear Logic

38 points by hoping1 156 days ago | 10 comments

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

190 points by ColinWright 168 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 172 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 175 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 175 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 205 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 206 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 223 days ago | 0 comments

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

Logic, History, Mathematics, Books

8 points by sandwichsphinx 227 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.