Related papers: An Automated Theorem Generator with Theoretical Fo…

Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…

Abstract reasoning, i.e., inferring complicated patterns from given observations, is a central building block of artificial general intelligence. While humans find the answer by either eliminating wrong candidates or first constructing the…

Recent advances in Large Language Models (LLMs) have significantly improved complex reasoning capabilities. Retrieval-Augmented Generation (RAG) has further extended these capabilities by grounding generation in dynamically retrieved…

The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…

Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…

The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…

In this paper, we present a framework for automatic generation of CHR solvers given the logical specification of the constraints. This approach takes advantage of the power of tabled resolution for constraint logic programming, in order to…

We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…

Automated Test Case Generation (ATCG) is crucial for evaluating software reliability, particularly in competitive programming where robust algorithm assessments depend on diverse and accurate test cases. However, existing ATCG methods often…

Retrieval-Augmented Generation (RAG) has been widely adopted to enhance Large Language Models (LLMs) in knowledge-intensive tasks. To enhance credibility and verifiability in RAG systems, Attributed Text Generation (ATG) is proposed, which…

Retrieval-Augmented Generation (RAG) has gained significant attention in recent years for its potential to enhance natural language understanding and generation by combining large-scale retrieval systems with generative models. RAG…

Retrieval-Augmented Generation (RAG) merges retrieval methods with deep learning advancements to address the static limitations of large language models (LLMs) by enabling the dynamic integration of up-to-date external information. This…

Agentic Generative AI, powered by Large Language Models (LLMs) with Retrieval-Augmented Generation (RAG), Knowledge Graphs (KGs), and Vector Stores (VSs), represents a transformative technology applicable to specialized domains such as…

We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-computational' proofs from the mainstream mathematical…

With the rise of prolific ChatGPT, the risk and consequences of AI-generated text has increased alarmingly. To address the inevitable question of ownership attribution for AI-generated artifacts, the US Copyright Office released a statement…

Large language models (LLMs) often suffer from hallucination, generating factually incorrect statements when handling questions beyond their knowledge and perception. Retrieval-augmented generation (RAG) addresses this by retrieving…

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…

We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…

Tremendous research effort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the different approaches is much…

A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…