相关论文: Constructive Galois Connections: Taming the Galois…
In implementing evaluation strategies of the lambda-calculus, both correctness and efficiency of implementation are valid concerns. While the notion of correctness is determined by the evaluation strategy, regarding efficiency there is a…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
interpretation is a general methodology for building static analyses of programs. It was introduced by P. and R. Cousot in \cite{cc}. We present, in this paper, an application of a generic abstract interpretation to domain of…
While concept-based interpretability methods have traditionally focused on local explanations of neural network predictions, we propose a novel framework and interactive tool that extends these methods into the domain of mechanistic…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
We present an expressive logic over trace formulas, based on binary state predicates, chop, and least fixed-points, for precise specification of programs with recursive procedures. Both, programs and trace formulas, are equipped with a…
We show how to smoothly incorporate in the object-oriented paradigm constructs to raise, compose, and handle effects in an arbitrary monad. The underlying pure calculus is meant to be a representative of the last generation of OO languages,…
This paper introduces a novel approach to understanding Galois theory, one of the foundational areas of algebra, through the lens of machine learning. By analyzing polynomial equations with machine learning techniques, we aim to streamline…
We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.
Analogical proportions are 4-ary relations that read "A is to B as C is to D". Recent works have highlighted the fact that such relations can support a specific form of inference, called analogical inference. This inference mechanism was…
Logical fallacy uses invalid or faulty reasoning in the construction of a statement. Despite the prevalence and harmfulness of logical fallacies, detecting and classifying logical fallacies still remains a challenging task. We observe that…
Generalized Additive Models (GAMs) are commonly considered *interpretable* within the ML community, as their structure makes the relationship between inputs and outputs relatively understandable. Therefore, it may seem natural to…
The use of generative AI to create text descriptions from graphs has mostly focused on knowledge graphs, which connect concepts using facts. In this work we explore the capability of large pretrained language models to generate text from…
This note illustrates how a variety of causal abstraction arXiv:1707.00819 arXiv:1812.03789, defined here as causal abstractive simulation, can be used to formalize a simple example of language model simulation. This note considers the case…
Given $\texttt{S}|\texttt{R}$ a finite Galois extension of finite chain rings and $\mathcal{B}$ an $\texttt{S}$-linear code we define two Galois operators, the closure operator and the interior operator. We proof that a linear code is…
Graph Neural Networks (GNNs) have become a powerful tool for modeling and analyzing data with graph structures. The wide adoption in numerous applications underscores the value of these models. However, the complexity of these methods often…
By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalise the traditional quantum-to-classical transition.…
Notions of guardedness serve to delineate admissible recursive definitions in various settings in a compositional manner. In recent work, we have introduced an axiomatic notion of guardedness in symmetric monoidal categories, which serves…
The paper presents algebraic and logical developments. From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation. From the logical viewpoint, we provide Equational…
We present an approach for the static analysis of programs handling arrays, with a Galois connection between the semantics of the array program and semantics of purely scalar operations. The simplest way to implement it is by automatic,…