Discrete Mathematics

discrete.openmathbooks.org

윤건영 “윤석열이 뜯어갔다, 1년 걸려 만든 청와대 지하 벙커”

윤석열 전 대통령이 용산에 대통령실을 구비하면서 청와대에 있던 지하 벙커(국가위기관리센터)를 “뜯어갔다”는 전언이 나왔다. 때문에 다시 대통령실을 청와대로 이전해 시스템을 회복하기까지 시간이 걸릴 거란 예측이다. 윤건영 더불어민주당 의원은 10일 문화방송(MBC) 라디

www.hani.co.kr · 한겨레

Are LLMs Reliable Translators of Logical Reasoning Across Lexically Diversified Contexts?

Neuro-symbolic approaches combining large language models (LLMs) with solvers excels in logical reasoning problems need long reasoning chains. In this paradigm, LLMs serve as translators, converting natural language reasoning problems into formal logic formulas. Then reliable symbolic solvers return correct solutions. Despite their success, we find that LLMs, as translators, struggle to handle lexical diversification, a common linguistic phenomenon, indicating that LLMs as logic translators are unreliable in real-world scenarios. Moreover, existing logical reasoning benchmarks lack lexical diversity, failing to challenge LLMs' ability to translate such text and thus obscuring this issue. In this work, we propose SCALe, a benchmark designed to address this significant gap through **logic-invariant lexical diversification**. By using LLMs to transform original benchmark datasets into lexically diversified but logically equivalent versions, we evaluate LLMs' ability to consistently map diverse expressions to uniform logical symbols on these new datasets. Experiments using SCALe further confirm that current LLMs exhibit deficiencies in this capability. Building directly on the deficiencies identified through our benchmark, we propose a new method, MenTaL, to address this limitation. This method guides LLMs to first construct a table unifying diverse expressions before performing translation. Applying MenTaL through in-context learning and supervised fine-tuning (SFT) significantly improves the performance of LLM translators on lexically diversified text. Our code is now available at https://github.com/wufeiwuwoshihua/LexicalDiver.

arxiv.org · arXiv.org

BBC Bosses Draw Up Plans to Win Over Reform Voters by Changing News and Drama Output

The Director General Tim Davie and other executives discussed altering BBC “story selection” in order to secure the "trust" of supporters of Nigel Farage’s party

bylinetimes.com · Byline Times

Safe: Enhancing Mathematical Reasoning in Large Language Models via Retrospective Step-aware Formal Verification

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework $Safe$. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework $Safe$ across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose $FormalStep$ as a benchmark for step correctness theorem proving with $30,809$ formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

arxiv.org · arXiv.org

FreeBSD 14.3-RELEASE Announcement

FreeBSD is an operating system used to power modern servers, desktops, and embedded platforms.

www.freebsd.org · The FreeBSD Project

PhD Position in Logics for Multi-Agent Systems

Interested in developing and applying logic to study accountability and responsibility in multi-agent systems? Join this exciting interdisciplinary project!

www.uu.nl · Utrecht University

FreeBSD 14.3-RELEASE Announcement

FreeBSD is an operating system used to power modern servers, desktops, and embedded platforms.

www.freebsd.org · The FreeBSD Project

Premise Selection for a Lean Hammer

Neural methods are transforming automated reasoning for proof assistants, yet integrating these advances into practical verification workflows remains challenging. Hammers are tools that interface with external automatic theorem provers to automate tedious reasoning steps. They have dramatically improved productivity in proof assistants, but the Lean proof assistant still does not have a hammer despite its growing popularity. We present LeanHammer, the first end-to-end domain-general hammer for Lean, built on a novel neural premise selection system for a hammer in dependent type theory. Unlike existing Lean premise selectors, our approach dynamically adapts to user-specific contexts and combines with symbolic proof search and reconstruction to create a practical hammer. With comprehensive evaluations, we show that our premise selector enables LeanHammer to solve 21\% more goals relative to existing premise selectors, and generalize well to diverse domains. Our work bridges the gap between neural retrieval and symbolic reasoning, making formal verification more accessible to researchers and practitioners.

arxiv.org · arXiv.org

Talking Heads Celebrate 50th Anniversary With 'Psycho Killer' Video Starring Saoirse Ronan

The video, directed by Mike Mills, coincides with the band's 50th anniversary.

www.rollingstone.com · Rolling Stone

Why agents are bad pair programmers

LLM agents make bad pairs because they code faster than humans think. I'll admit, I've had a lot of fun using GitHub Copilot's agent mode in VS Code this month.…

justin.searls.co · justin․searls․co

Inductive definitions

lawrencecpaulson.github.io

How to import() a JavaScript String—zachleat.com

A post by Zach Leatherman (zachleat)

www.zachleat.com · Zach Leatherman

The weaponization of Waymo

How protestors turned torched Waymos into icons of the anti-ICE demonstrations

www.bloodinthemachine.com

Readings shared June 9, 2025

The readings shared in Bluesky on 9 June 2025 are Formalizing invisible mathematics: case studies from higher category theory. ~ Emily Riehl. #ITP #LeanProver #Math #CategoryTheory Sequencelib: A pla

jaalonso.github.io · Vestigium

The weaponization of Waymo

How protestors turned torched Waymos into icons of the anti-ICE demonstrations

www.bloodinthemachine.com

Using the quantum-secure APIs | Apple Developer Documentation

Enhance your app’s privacy and security by using quantum-secure workflows.

docs.developer.apple.com · Apple Developer Documentation

Hands on with Python t-strings

Showcasing a new feature in Python 3.14 - "t-strings".t-strings are way of composing templates in Python, to customize what you would otherwise do in f-strin...

www.youtube.com · YouTube

Understanding the Metal 4 core API | Apple Developer Documentation

Discover the features and functionality in the Metal 4 foundational APIs.

docs.developer.apple.com · Apple Developer Documentation

Understanding the Metal 4 core API | Apple Developer Documentation

Discover the features and functionality in the Metal 4 foundational APIs.

docs.developer.apple.com · Apple Developer Documentation

FreeBSD 14.3-RELEASE Release Notes

FreeBSD is an operating system used to power modern servers, desktops, and embedded platforms.

www.freebsd.org · The FreeBSD Project

Catalin Cimpanu (@campuscodi@mastodon.social)

Russian border authorities are denying entry to Ukrainians with clean phones. According to court documents, authorities denied entry to users who wiped their image galleries, messenger chats, or deleted their YouTube watch history https://ria.ru/20250608/prichiny-2021606520.html

mastodon.social · Mastodon

“LA 군 투입, 계엄령의 서곡”…트럼프가 노리는 것

“트럼프에게 이것은 예행연습이다.” 트럼프 대통령이 주방위군을 로스앤젤레스에 투입한 것을 두고 ‘계엄령’을 겨냥한 예행연습이라는 의혹이 일고 있다. 자신의 집권에 위협이 감지될 경우, 어떻게 군을 동원해 대응할 수 있을지 ‘시나리오’를 미리 시험해 보고 있다는 것이다.

www.hani.co.kr · 한겨레