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The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other…
Large language models (LLMs) offer significant potential to accelerate systematic literature reviews (SLRs), yet current approaches often rely on brittle, manually crafted prompts that compromise reliability and reproducibility. This…
Brzozowski derivatives of a regular expression are developed for constructing deterministic automata from the given regular expression in the algebraic way. In this paper,some lemmas of the regular expressions are discussed and the regular…
Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing…
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…
The remarkable success of pretrained language models has motivated the study of what kinds of knowledge these models learn during pretraining. Reformulating tasks as fill-in-the-blanks problems (e.g., cloze tests) is a natural approach for…
Large Language Models (LLMs) are promising analytical tools. They can augment human epistemic, cognitive and reasoning abilities, and support 'sensemaking', making sense of a complex environment or subject by analysing large volumes of data…
Large Language Models (LLMs) are often used as automated judges to evaluate text, but their effectiveness can be hindered by various unintentional biases. We propose using linear classifying probes, trained by leveraging differences between…
Creativity, or the ability to produce new useful ideas, is commonly associated to the human being; but there are many other examples in nature where this phenomenon can be observed. Inspired by this fact, in engineering and particularly in…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce $\emph{FERMAT}$, a reinforcement learning (RL) environment that models concept…
Given the remarkable performance of Large Language Models (LLMs), an important question arises: Can LLMs conduct human-like scientific research and discover new knowledge, and act as an AI scientist? Scientific discovery is an iterative…
We present a new approach for benchmarking Large Language Model (LLM) capabilities on research-level mathematics. Existing benchmarks largely rely on static, hand-curated sets of contest or textbook-style problems as proxies for…
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…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
Automatic extraction of procedural graphs from documents creates a low-cost way for users to easily understand a complex procedure by skimming visual graphs. Despite the progress in recent studies, it remains unanswered: whether the…
The Lov\'{a}sz Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser and Tardos and follow-up works…
Causal structure discovery from observations can be improved by integrating background knowledge provided by an expert to reduce the hypothesis space. Recently, Large Language Models (LLMs) have begun to be considered as sources of prior…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Recently, it is often said that the data used for the pre-training of large language models (LLMs) have been exhausted. This paper proposes a solution to the problem: Automated generation of massive reasonable empirical theorems by forward…