Related papers: A Novice-Friendly Induction Tactic for Lean
Counterfactual reasoning, a hallmark of intelligence, consists of three steps: inferring latent variables from observations (abduction), constructing alternatives (interventions), and predicting their outcomes (prediction). This skill is…
Inductive reasoning enables humans to infer abstract rules from limited examples and apply them to novel situations. In this work, we compare an LLM-based hypothesis search framework with direct program generation approaches on few-shot…
Lean is an increasingly popular proof assistant based on dependent type theory. Despite its success, it still lacks important automation features present in more seasoned proof assistants, such as the Sledgehammer tactic in Isabelle/HOL. A…
Hypothesis tests under order restrictions arise in a wide range of scientific applications. By exploiting inequality constraints, such tests can achieve substantial gains in power and interpretability. However, these gains come at a cost:…
Modern large language models (LLMs) are capable of interpreting input strings as instructions, or prompts, and carry out tasks based on them. Unlike traditional learners, LLMs cannot use back-propagation to obtain feedback, and condition…
Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to…
Numerous works are proposed to align large language models (LLMs) with human intents to better fulfill instructions, ensuring they are trustful and helpful. Nevertheless, some human instructions are often malicious or misleading and…
Common criticisms of state-of-the-art machine learning include poor generalisation, a lack of interpretability, and a need for large amounts of training data. We survey recent work in inductive logic programming (ILP), a form of machine…
Autoregressive Large Language Models have transformed the landscape of Natural Language Processing. Pre-train and prompt paradigm has replaced the conventional approach of pre-training and fine-tuning for many downstream NLP tasks. This…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
The physics community relies on index notation to effectively manipulate types of tensors. This paper introduces the first formally verified implementation of index notation in the interactive theorem prover Lean 4. By integrating index…
Explainability and effectiveness are two key aspects for building recommender systems. Prior efforts mostly focus on incorporating side information to achieve better recommendation performance. However, these methods have some weaknesses:…
Scientists form hypotheses and experimentally test them. If a hypothesis fails (is refuted), scientists try to explain the failure to eliminate other hypotheses. The more precise the failure analysis the more hypotheses can be eliminated.…
We present a new technique for automatically inferring inductive invariants of parameterized distributed protocols specified in TLA+. Ours is the first such invariant inference technique to work directly on TLA+, an expressive, high level…
We present Tactician, a tactic learner and prover for the Coq Proof Assistant. Tactician helps users make tactical proof decisions while they retain control over the general proof strategy. To this end, Tactician learns from previously…
Previous theoretical results pertaining to meta-learning on sequences build on contrived assumptions and are somewhat convoluted. We introduce new information-theoretic tools that lead to an elegant and very general decomposition of error…
There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing…
The growing adoption of generative AI in education highlights the need to integrate established pedagogical principles into AI-assisted learning environments. This study investigates the potential of metacognitive theory to inform…
The diverse views of science of security have opened up several alleys towards applying the methods of science to security. We pursue a different kind of connection between science and security. This paper explores the idea that security is…
Protothetic is one of the most stimulating systems for propositional logic. Including quantifiers and an inference rule for definitions, it is a very interesting mean for the study of many questions of metalogic. Unfortunately, it only…