Related papers: An Automated Theorem Generator with Theoretical Fo…
Humans can develop new theorems to explore broader and more complex mathematical results. While current generative language models (LMs) have achieved significant improvement in automatically proving theorems, their ability to generate new…
Trustworthy AI requires reasoning systems that are not only powerful but also transparent and reliable. Automated Theorem Proving (ATP) is central to formal reasoning, yet classical binary resolution remains limited, as each step involves…
Automated deduction lies at the core of Artificial Intelligence (AI), underpinning theorem proving, formal verification, and logical reasoning. Despite decades of progress, reconciling deductive completeness with computational efficiency…
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…
We introduce a novel data generation method for contradiction detection, which leverages the generative power of large language models as well as linguistic rules. Our vision is to provide a condensed corpus of prototypical contradictions,…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve…
The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a…
Large Language Models (LLMs) have great potential to accelerate and support scholarly peer review and are increasingly used as fully automatic review generators (ARGs). However, potential biases and systematic errors may pose significant…
Large language models (LLMs) have significantly advanced formal theorem proving, yet the scarcity of high-quality training data constrains their capabilities in complex mathematical domains. Combinatorics, a cornerstone of mathematics,…
Controlled text generation (CTG) seeks to guide large language model (LLM) output to produce text that conforms to desired criteria. The current study presents a novel CTG algorithm that enforces adherence toward specific rhetorical…
The rapid development of Artificial Intelligence (AI) has led to the creation of powerful text generation models, such as large language models (LLMs), which are widely used for diverse applications. However, concerns surrounding…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
Automated Theorem Proving (ATP) is an established branch of Artificial Intelligence. The purpose of ATP is to design a system which can automatically figure out an algorithm either to prove or disprove a mathematical claim, on the basis of…
Text generative models (TGMs) excel in producing text that matches the style of human language reasonably well. Such TGMs can be misused by adversaries, e.g., by automatically generating fake news and fake product reviews that can look…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
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…
Natural Language Processing and Generation systems have recently shown the potential to complement and streamline the costly and time-consuming job of professional fact-checkers. In this work, we lift several constraints of current…