Related papers: Towards Machine Learning Induction
Machine learning (ML) methods have been developing rapidly, but configuring and selecting proper methods to achieve a desired performance is increasingly difficult and tedious. To address this challenge, automated machine learning (AutoML)…
Like any field of empirical science, AI may be approached axiomatically. We formulate requirements for a general-purpose, human-level AI system in terms of postulates. We review the methodology of deep learning, examining the explicit and…
Mathematical induction is a fundamental tool in computer science and mathematics. Henkin initiated the study of formalization of mathematical induction restricted to the setting when the base case B is set to singleton set containing 0 and…
We report on several scenarios of using automated theorem proving software in university education. In particular, we focus on using the Theorema system in a software-enhanced logic-course for students in computer science or artificial…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
Existing approaches to learning to prove theorems focus on particular logics and datasets. In this work, we propose Monte-Carlo simulations guided by reinforcement learning that can work in an arbitrarily specified logic, without any human…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
As AI systems become increasingly autonomous, aligning their decision-making to human preferences is essential. In domains like autonomous driving or robotics, it is impossible to write down the reward function representing these…
The emergence and continued reliance on the Internet and related technologies has resulted in the generation of large amounts of data that can be made available for analyses. However, humans do not possess the cognitive capabilities to…
Science consists on conceiving hypotheses, confronting them with empirical evidence, and keeping only hypotheses which have not yet been falsified. Under deductive reasoning they are conceived in view of a theory and confronted with…
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
Inductive logic programming (ILP) is a form of logic-based machine learning. The goal is to induce a hypothesis (a logic program) that generalises given training examples. As ILP turns 30, we review the last decade of research. We focus on…
We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts.…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of…
Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…
Cell injection is an approach used for the delivery of small sample substances into a biological cell and is widely used in drug development, gene injection, intracytoplasmic sperm injection (ICSI) and in-virto fertilization (IVF). Robotic…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…