Related papers: Update report: LEO-II version 1.5
This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL…
A recent line of works apply machine learning techniques to assist or rebuild cost-based query optimizers in DBMS. While exhibiting superiority in some benchmarks, their deficiencies, e.g., unstable performance, high training cost, and slow…
Large language models (LLMs) exhibit remarkable capabilities across diverse tasks, yet aligning them efficiently and effectively with human expectations remains a critical challenge. This thesis advances LLM alignment by introducing novel…
Large language models have demonstrated remarkable capabilities, but their performance is heavily reliant on effective prompt engineering. Automatic prompt optimization (APO) methods are designed to automate this and can be broadly…
Prompt optimization has often been framed as a discrete search problem to find high-performing and robust instructions for an LLM. However, the search result might not make it transparent why and where specific prompt changes lead to…
Automating the translation of natural language to first-order logic (FOL) is crucial for knowledge representation and formal methods, yet remains challenging. We present a systematic evaluation of fine-tuned LLMs for this task, comparing…
Since the release of T\"ULU [Wang et al., 2023b], open resources for instruction tuning have developed quickly, from better base models to new finetuning techniques. We test and incorporate a number of these advances into T\"ULU, resulting…
We introduce our Leanabell-Prover-V2, a 7B large language models (LLMs) that can produce formal theorem proofs in Lean 4, with verifier-integrated Long Chain-of-Thoughts (CoT). Following our previous work Leanabell-Prover-V1, we continual…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
The result in theorem 2.1 has been strengthened (see theorem 2.3) and the remarks in the introduction and the text adapted to this new result. Also some misprints in the previous version have been corrected.
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
Evolutionary agentic systems intensify the trade-off between computational efficiency and reasoning capability by repeatedly invoking large language models (LLMs) during inference. This setting raises a central question: how can an agent…
We describe an extension to the TLA+ specification language with constructs for writing proofs and a proof environment, called the Proof Manager (PM), to checks those proofs. The language and the PM support the incremental development and…
Modern saturation-based Automated Theorem Provers typically implement the superposition calculus for reasoning about first-order logic with or without equality. Practical implementations of this calculus use a variety of literal selections…
The algorithm selection problem is to choose the most suitable algorithm for solving a given problem instance. It leverages the complementarity between different approaches that is present in many areas of AI. We report on the state of the…
Large language models (LLMs) have shown promising abilities as cost-effective and reference-free evaluators for assessing language generation quality. In particular, pairwise LLM evaluators, which compare two generated texts and determine…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…