Related papers: Nonuniform Coercions via Unification Hints
This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…
In this paper, we show that Higher-Order Coloured Unification - a form of unification developed for automated theorem proving - provides a general theory for modeling the interface between the interpretation process and other sources of…
While the traditional conception of inductive logic is Carnapian, I develop a Peircean alternative and use it to unify formal learning theory, statistics, and a significant part of machine learning: supervised learning. Some crucial…
Within intelligent tutoring systems, considerable research has investigated hints, including how to generate data-driven hints, what hint content to present, and when to provide hints for optimal learning outcomes. However, less attention…
This paper introduces norm_cast, a toolbox of tactics for the Lean proof assistant designed to manipulate expressions containing coercions and casts. These expressions can be frustrating for beginning and expert users alike; the presence of…
Recent work has demonstrated that problems-- particularly imitation learning and structured prediction-- where a learner's predictions influence the input-distribution it is tested on can be naturally addressed by an interactive approach…
We introduce a new class of extensions of terms that consists in navigation strategies and insertion of contexts. We introduce an operation of combination on this class which is associative, admits a neutral element and so that each…
The use of multivariate classifiers, especially neural networks and decision trees, has become commonplace in particle physics. Typically, a series of classifiers is trained rather than just one to enhance the performance; this is known as…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
Machine learning models are increasingly deployed for critical decision-making tasks, making it important to verify that they do not contain gender or racial biases picked up from training data. Typical approaches to achieve fairness…
We introduce the notion of identity coercions between non-indexed and indexed variants of inductive datatypes, such as lists and vectors. An identity coercion translates one type to another such that the coercion function definitionally…
Interactive proofs are often considered as costs of formal modelling activity. In an incremental development environment such as the Rodin platform for Event-B, information from proof attempts is important input for adapting the model. This…
The unification type of an equational theory is defined using a preorder on substitutions, called the instantiation preorder, whose scope is either restricted to the variables occurring in the unification problem, or unrestricted such that…
Inequities in student access to trigonometry and calculus are often associated with racial and socioeconomic privilege, and often influence introductory physics course performance. To mitigate these disparities in student preparedness, we…
Data augmentation is widely used in vision to introduce variation and mitigate overfitting, by enabling models to learn invariant properties. However, augmentation only indirectly captures these properties and does not explicitly constrain…
Many real world learning tasks involve complex or hard-to-specify objectives, and using an easier-to-specify proxy can lead to poor performance or misaligned behavior. One solution is to have humans provide a training signal by…
We describe a general method for verifying inequalities between real-valued expressions, especially the kinds of straightforward inferences that arise in interactive theorem proving. In contrast to approaches that aim to be complete with…
Modelling uncertainty in Machine Learning models is essential for achieving safe and reliable predictions. Most research on uncertainty focuses on output uncertainty (predictions), but minimal attention is paid to uncertainty at inputs. We…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
An extension to classical unification, called {\em graded unification} is presented. It is capable of combining contradictory information. An interactive processing paradigm and parser based on this new operator are also presented.