logic

This paper examines intensional anaphora, arguing that description-based presuppositions better account for pronoun licensing than existing value-based accounts, and formalizes the proposal in a new logic called Plural Intensional Presuppositional predicate calculus (PIP).

This paper investigates how different formal knowledge representation notations affect language models' syllogistic reasoning, extending FOLIO and P-FOLIO datasets and introducing the CLGC library for generating syllogisms.

An accessible explanation of Gödel's incompleteness theorems, describing how Gödel numbering maps statements about a system onto statements within the system to prove that any consistent axiomatic system is incomplete.

This theoretical paper studies atomic concept learning through the geometry of hypercubes and hyperplanes, showing that complexity collapses uniformly on most hyperplanes except the full diagonal, where it grows without bound. It provides a taxonomy of hyperplane behavior and a worked binary and ternary case analysis.

A practical book introducing logic for programmers to improve software design, verification, and reasoning, covering topics from simplifying conditionals to formal verification and constraint solving.

Hillel Wayne announces the completion and 1.0 release of his book 'Logic for Programmers', a guide to using logic in software development, now available in print and as a free update for early ebook buyers.

The Incredible Proof Machine is a visual tool for performing proofs in various logics by dragging and connecting blocks. It aims to make theorem proving accessible and fun without needing syntax of traditional provers.

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.