Related papers: Abstraction boundaries and spec driven development…
The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…
A self-contained introduction is presented of the notion of the (abstract) differentiable manifold and its tangent vector fields. The way in which elementary topological ideas stimulated the passage from Euclidean (vector) spaces and linear…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
Explanations of cognitive behavior often appeal to computations over representations. What does it take for a system to implement a given computation over suitable representational vehicles within that system? We argue that the language of…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
In this paper, our aim is to propose a model for code abstraction, based on abstract interpretation, allowing us to improve the precision of a recently proposed static analysis by abstract interpretation of dynamic languages. The problem we…
Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives,…
The evaluation of mathematical results plays a central role in assessing researchers' contributions and shaping the direction of the field. Currently, such evaluations rely primarily on human judgment, whether through journal peer review or…
Abstraction is a key verification technique to improve scalability. However, its use for neural networks is so far extremely limited. Previous approaches for abstracting classification networks replace several neurons with one of them that…
interpreters are tools to compute approximations for behaviors of a program. These approximations can then be used for optimisation or for error detection. In this paper, we show how to describe an abstract interpreter using the type-theory…
Neural network models have shown excellent fluency and performance when applied to abstractive summarization. Many approaches to neural abstractive summarization involve the introduction of significant inductive bias, exemplified through…
Structural causal models provide a formalism to express causal relations between variables of interest. Models and variables can represent a system at different levels of abstraction, whereby relations may be coarsened and refined according…
The study of causal abstractions bridges two integral components of human intelligence: the ability to determine cause and effect, and the ability to interpret complex patterns into abstract concepts. Formally, causal abstraction frameworks…
Convex polyhedral abstractions of logic programs have been found very useful in deriving numeric relationships between program arguments in order to prove program properties and in other areas such as termination and complexity analysis. We…
Large Language Models (LLMs) often struggle with deductive judgment in syllogistic reasoning, systematically conflating semantic plausibility with formal validity a phenomenon known as content effect. This bias persists even when models…
Abductive explanations (AXp's) are widely used for understanding decisions of classifiers. Existing definitions are suitable when features are independent. However, we show that ignoring constraints when they exist between features may lead…
The technique of abstracting abstract machines (AAM) provides a systematic approach for deriving computable approximations of evaluators that are easily proved sound. This article contributes a complementary step-by-step process for…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…