Related papers: Improving the Competency of First-Order Ontologies

In this note we observe that automated theorem provers (ATPs) that recursively enumerate theorems in a particular way will fail to identify some valid theorems for a reason that is analogous to how G\"odel proved the existence of what are…

There is an increasing interest in applying recent advances in AI to automated reasoning, as it may provide useful heuristics in reasoning over formalisms in first-order, second-order, or even meta-logics. To facilitate this research, we…

Training Large Language Models (LLMs) for chain-of-thought reasoning presents a significant challenge: supervised fine-tuning on a single "golden" rationale hurts generalization as it penalizes equally valid alternatives, whereas…

Aiming at efficient and dense chain-of-thought (CoT) reasoning, latent reasoning methods fine-tune Large Language Models (LLMs) to substitute discrete language tokens with continuous latent tokens. These methods consume fewer tokens…

The recent development of chain-of-thought (CoT) decoding has enabled large language models (LLMs) to generate explicit logical reasoning paths for complex problem-solving. However, research indicates that these paths are not always…

Paraphrasing re-expresses meaning to enhance applications like text simplification, machine translation, and question-answering. Specific paraphrase types facilitate accurate semantic analysis and robust language models. However, existing…

Direct Preference Optimization (DPO) has gained significant attention for its simplicity and computational efficiency in aligning large language models (LLMs). Recent advancements have extended DPO to multimodal scenarios, achieving strong…

Large language models (LLMs) have revolutionized natural language processing by solving a wide range of tasks simply guided by a prompt. Yet their performance is highly sensitive to prompt formulation. While automatic prompt optimization…

Large Language Models (LLMs) still struggle with complex logical reasoning. While previous works achieve remarkable improvements, their performance is highly dependent on the correctness of translating natural language (NL) problems into a…

This paper presents the Personalized Thinking Model (PTM), a hierarchical and interpretable learner representation designed for AI supported education. PTM organizes evidence from learner journals into a five-layer structure covering…

We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…

First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an…

We make three contributions. First, we formulate a discussion-graph semantics for first-order logic with equality, enabling reasoning about discussion and argumentation in AI more generally than before. This addresses the current lack of a…

Today, the dominant paradigm for training neural networks involves minimizing task loss on a large dataset. Using world knowledge to inform a model, and yet retain the ability to perform end-to-end training remains an open question. In this…

We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…

Formal, automated theorem proving has long been viewed as a challenge to artificial intelligence. We introduce here a new approach to computer theorem proving, one that employs specialized language models for Lean4 proof generation combined…

In the logical framework introduced by Grohe and Tur\'an (TOCS 2004) for Boolean classification problems, the instances to classify are tuples from a logical structure, and Boolean classifiers are described by parametric models based on…

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…

This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms. The formalisms are in higher-order logic (with and without type…

Analogy is one of the core capacities of human cognition; when faced with new situations, we often transfer prior experience from other domains. Most work on computational analogy relies heavily on complex, manually crafted input. In this…