Related papers: Learning from {\L}ukasiewicz and Meredith: Investi…

We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for…

This paper explores a top-down approach to automating incremental advances in machine learning research through component-level innovation, facilitated by Large Language Models (LLMs). Our framework systematically generates novel…

In this paper, we present an experiment of our randomized hints strategy of automated reasoning for yielding Axiom(5) from Axiom(1)(2)(3)(4) of Infinite-Valued Lukasiewicz Logic. In the experiment, we randomly generated a set of hints with…

In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics).…

We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…

In logical reasoning, it is often the case that only some of a collection of assumptions are needed to reach a conclusion. A strengthening lemma is an assertion that a given conclusion is independent in this sense of a particular…

With recent advances in large language models (LLMs), the concept of automatically generating children's educational materials has become increasingly realistic. Working toward the goal of age-appropriate simplicity in generated educational…

The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…

Large Language Models (LLMs) have the potential to revolutionize automated traceability by overcoming the challenges faced by previous methods and introducing new possibilities. However, the optimal utilization of LLMs for automated…

We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.

Large language models (LLMs) increasingly help people solve problems, from debugging code to repairing machinery. This process requires generating plausible hypotheses from partial descriptions, then updating them as more information…

Assessing the veracity of online content has become increasingly critical. Large language models (LLMs) have recently enabled substantial progress in automated veracity assessment, including automated fact-checking and claim verification…

Scientific discovery in biology is difficult due to the complexity of the systems involved and the expense of obtaining high quality experimental data. Automated techniques are a promising way to make scientific discoveries at the scale and…

Although LLMs have shown great performance on Mathematics and Coding related reasoning tasks, the reasoning capabilities of LLMs regarding other forms of reasoning are still an open problem. Here, we examine the issue of reasoning from the…

Cut-introduction is a technique for structuring and compressing formal proofs. In this paper we generalize our cut-introduction method for the introduction of quantified lemmas of the form $\forall x.A$ (for quantifier-free $A$) to a method…

Large language models (LLMs) have shown impressive capabilities across a wide range of language tasks. However, their reasoning process is primarily guided by statistical patterns in training data, which limits their ability to handle novel…

Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the…

Inconsistencies are ubiquitous in law, administration, and jurisprudence. Though a cure is too much to hope for, we propose a technological remedy. Large language models (LLMs) can accurately extract propositions from arguments and compile…

Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level…

Property checking of RTL designs is a central task in formal verification. Among available engines, IC3/PDR is a widely used backbone whose performance critically depends on inductive generalization, the step that generalizes a concrete…