Related papers: Theory Exploration Powered By Deductive Synthesis

Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…

Large language models have achieved remarkable success in general language understanding tasks. However, as a family of generative methods with the objective of next token prediction, the semantic evolution with the depth of these models…

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…

The application of Large Language Models to Question Answering has shown great promise, but important challenges such as hallucinations and erroneous reasoning arise when using these models, particularly in knowledge-intensive,…

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…

A default theory can be characterized by its sets of plausible conclusions, called its extensions. But, due to the theoretical complexity of Default Logic (Sigma_2p-complete), the problem of finding such an extension is very difficult if…

Since the advent of Large Language Models (LLMs), efforts have largely focused on improving their instruction-following and deductive reasoning abilities, leaving open the question of whether these models can truly discover new knowledge.…

In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks, particularly when augmented with search mechanisms that enable systematic exploration of external knowledge bases. The field has evolved from…

Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…

Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we…

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…

Large Language Models (LLMs) are transforming scientific hypothesis generation and validation by enabling information synthesis, latent relationship discovery, and reasoning augmentation. This survey provides a structured overview of…

Developing the logic necessary to solve mathematical problems or write mathematical proofs is one of the more difficult objectives for large language models (LLMS). Currently, the most popular methods in literature consists of fine-tuning…

Mathematicians and computer scientists are increasingly using proof assistants to formalize and check correctness of complex proofs. This is a non-trivial task in itself, however, with high demands on human expertise. Can we lower the bar…

In some theory development tasks, a problem is satisfactorily solved once it is shown that a theorem (conjecture) is derivable from the background theory (premises). Depending on one's motivations, the details of the derivation of the…

Materials discovery requires navigating vast chemical and structural spaces while satisfying multiple, often conflicting, objectives. We present LLM-guided Evolution for MAterials discovery (LLEMA), a unified framework that couples the…

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…

Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…

Large language models (LLMs) are introducing a paradigm shift in molecular discovery by enabling text-guided interaction with chemical spaces through natural language, symbolic notations, with emerging extensions to incorporate multi-modal…