Related papers: Theory Exploration Powered By Deductive Synthesis
We address a not-widely-recognized subset of exploratory search, where a user sets out on a typically long "search quest" for the perfect wedding dress, overlooked research topic, killer company idea, etc. The first few outputs of current…
Refinement based formal methods allow the modelling of systems through incremental steps via abstraction. Discovering the right levels of abstraction, formulating correct and meaningful invariants, and analysing faulty models are some of…
As LLMs make their way into many aspects of our lives, one place that warrants increased scrutiny with LLM usage is scientific research. Using LLMs for generating or analyzing data for research purposes is gaining popularity. But when such…
Equation discovery is aimed at directly extracting physical laws from data and has emerged as a pivotal research domain. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require the design of…
This paper examines the problems faced by Law Enforcement in searching large quantities of electronic evidence. It examines the use of ontologies as the basis for new forensic software filters and provides a proof of concept tool based on…
A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…
Large language models (LLMs) have shown potential in assisting scientific research, yet their ability to discover high-quality research hypotheses remains unexamined due to the lack of a dedicated benchmark. To address this gap, we…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e. proof steps) to search through proof states. The current model, while trained solely on successful…
Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…
We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods…
Recommender systems are widely used to suggest engaging content, and Large Language Models (LLMs) have given rise to generative recommenders. Such systems can directly generate items, including for open-set tasks like question suggestion.…
Recursively defined linked data structures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) with background theories. Such logics, unlike pure…
This paper presents an in-depth analysis of Large Language Models (LLMs), focusing on LLaMA, a prominent open-source foundational model in natural language processing. Instead of assessing LLaMA through its generative output, we design…
As the significance of understanding the cause-and-effect relationships among variables increases in the development of modern systems and algorithms, learning causality from observational data has become a preferred and efficient approach…
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…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
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…