Related papers: Theory Exploration Powered By Deductive Synthesis

While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…

This research idea paper proposes leveraging Large Language Models (LLMs) to enhance the productivity of Dafny developers. Although the use of verification-aware languages, such as Dafny, has increased considerably in the last decade, these…

We present evidence of substantial benefit from efficient exploration in gathering human feedback to improve large language models. In our experiments, an agent sequentially generates queries while fitting a reward model to the feedback…

Generative molecular design has moved from proof-of-concept to real-world applicability, as marked by the surge in very recent papers reporting experimental validation. Key challenges in explainability and sample efficiency present…

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…

Exploration has been a crucial part of reinforcement learning, yet several important questions concerning exploration efficiency are still not answered satisfactorily by existing analytical frameworks. These questions include exploration…

Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We…

Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works and…

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…

In real practice, questions are typically complex and knowledge-intensive, requiring Large Language Models (LLMs) to recognize the multifaceted nature of the question and reason across multiple information sources. Iterative and adaptive…

Distilling underlying principles from data has historically driven scientific breakthroughs. However, conventional data-driven machine learning often produces complex models that lack interpretability and generalization due to insufficient…

Agentic theorem provers often introduce intermediate lemmas, proof sketches, or subgoal decompositions before returning to tactic-level search. This can look like an expensive detour: if proving lemmas is itself hard, why should a learned…

We present a system for bottom-up cumulative learning of myriad concepts corresponding to meaningful character strings, and their part-related and prediction edges. The learning is self-supervised in that the concepts discovered are used as…

The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…

Motivated by certain applications from physics, biochemistry, economics, and computer science, in which the objects under investigation are not accessible because of various limitations, we propose a trial-and-error model to examine…

Among the biggest challenges in property-based testing (PBT) is the constrained random generation problem: given a predicate on program values, randomly sample from the set of all values satisfying that predicate, and only those values.…

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…

Taxonomies are an important ingredient of knowledge organization, and serve as a backbone for more sophisticated knowledge representations in intelligent systems, such as formal ontologies. However, building taxonomies manually is a costly…

One of the fundamental challenges in reinforcement learning (RL) is to take a complex task and be able to decompose it to subtasks that are simpler for the RL agent to learn. In this paper, we report on our work that would identify subtasks…

In a previously published ENTCS paper (Santos et al. (2016)), we introduced a sequent calculus called $\mathbf{LMT^{\rightarrow}}$ for Minimal Implicational Propositional Logic ($\mathbf{LMT^{\rightarrow}}$). This calculus provides a proof…