logic

This paper surveys the historical and ongoing synergy between logic and optimization in AI, arguing that rule-based approaches enhanced by optimization solvers can provide transparency, explainability, and trustworthiness in contrast to purely connectionist methods.

This paper proposes a probabilistic extension to neuro-symbolic AGI robots using Belnap's typed intensional first-order logic. It introduces global and local symmetry transformations to preserve knowledge and enable real-time decisions, with neural networks computing probability density based on maximum information entropy.

Article discusses confusion regarding the logical consistency and reasoning abilities of AI chatbots.

This paper discusses how to make sense of proof by contradiction, a fundamental mathematical reasoning technique, for educational purposes.

Hillel Wayne announces version 0.15 release candidate of his book 'Logic for Programmers', and highlights a livecoding meetup featuring Strudel and CLAVIER-36 for music programming.

This paper traces the origin and history of the Muddy Children Puzzle, a classic epistemic logic puzzle, through publications spanning two centuries, and presents a novel hats puzzle involving self-reference.

AI has progressed to the point of contributing to original mathematical research, outperforming human mathematicians and potentially reducing demand for the profession, though human-AI teams may ultimately excel.

Hillel Wayne announces supplementary chapters for his book 'Logic for Programmers', covering topics like concurrent processes, first-order logic, Liskov's history rule, and orders.

An overview of the frame problem in AI and philosophy, tracing its origin as a technical issue in logic-based AI and its broader reinterpretation by philosophers of mind.

This paper investigates Neutrosophic Logic as a framework for modeling epistemic states in Large Language Models, demonstrating that it can capture 'hyper-truth' states beyond traditional probability constraints, leading to more transparent and ethically aware AI systems.

This paper introduces LGMT, a framework that uses first-order logic to generate semantically invariant test cases for evaluating LLM reasoning reliability. Experiments on six LLMs show that LGMT exposes hidden defects missed by static benchmarks, suggesting evaluation should focus on robustness under logical invariance.

An exploration of the meaning and implications of Gödel's incompleteness theorems, featuring insights from logicians, mathematicians, philosophers, and a physicist on how these theorems challenge the axiomatic method and the nature of mathematical truth.

Introduces LoVer, an unsupervised verifier that uses logical rules (negation consistency, intra-group and inter-group consistency) to improve LLM reasoning without labeled data, achieving performance close to supervised verifiers on reasoning benchmarks.

Hillel Wayne shares Z3 scripts he wrote, discussing challenges with logical properties and the concept of 'chaff' from his upcoming book Logic for Programmers.

Hillel Wayne announces the v0.13 release of his book 'Logic for Programmers', with significant rewrites and new content, and outlines next steps toward a print edition.