Related papers: An intensionally fully-abstract sheaf model for $\…
Interpretability and transparency are essential for incorporating causal effect models from observational data into policy decision-making. They can provide trust for the model in the absence of ground truth labels to evaluate the accuracy…
In heap-based languages, knowing that a variable x points to an acyclic data structure is useful for analyzing termination: this information guarantees that the depth of the data structure to which x points is greater than the depth of the…
The complexity of large-scale distributed systems, particularly when deployed in physical space, calls for new mechanisms to address composability and reusability of collective adaptive behaviour. Computational fields have been proposed as…
The $\pi$-calculus is a process algebra where agents interact by sending communication links to each other via noiseless communication channels. Taking into account the reality of noisy channels, an extension of the $\pi$-calculus, called…
This paper makes contributions to ``pure'' sheaf model theory, the part of model theory in which the models are sheaves over a complete Heyting algebra. We start by outlining the theory in a way we hope is readable for the non-specialist.…
Explainable Artificial Intelligence (XAI) techniques, such as SHapley Additive exPlanations (SHAP), have become essential tools for interpreting complex ensemble tree-based models, especially in high-stakes domains such as healthcare…
One of the aims of Implicit Computational Complexity is the design of programming languages with bounded computational complexity; indeed, guaranteeing and certifying a limited resources usage is of central importance for various aspects of…
We propose a type-based resource usage analysis for the π-calculus extended with resource creation/access primitives. The goal of the resource usage analysis is to statically check that a program accesses resources such as files and…
The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus modulo. We show in this paper that this simple extension…
We aim to use the concept of sheaf to establish a link between certain aspects of the set of positive integers numbers, a topic corresponding to the elementary mathematics, and some fundamental ideas of contemporary mathematics. We hope…
Axioms are presented which encapsulate the properties satisfied by categories of games which form the basis of results on full abstraction for PCF and other programming languages, and on full completeness for various logics and type…
Theoretical foundations of compositional reasoning about heaps in imperative programming languages are investigated. We introduce a novel concept of compositional symbolic memory and its relevant properties. We utilize these formal…
According to a mainstream position in contemporary cognitive science and philosophy, the use of abstract compositional concepts is both a necessary and a sufficient condition for the presence of genuine thought. In this article, we show how…
We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…
The overarching goal of Explainable AI is to develop systems that not only exhibit intelligent behaviours, but also are able to explain their rationale and reveal insights. In explainable machine learning, methods that produce a high level…
We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…
We present a formalisation in Agda of the theory of concurrent transitions, residuation, and causal equivalence of traces for the pi-calculus. Our formalisation employs de Bruijn indices and dependently-typed syntax, and aligns the "proved…
We provide a compositional coalgebraic semantics for strategic games. In our framework, like in the semantics of functional programming languages, coalgebras represent the observable behaviour of systems derived from the behaviour of the…
The S-pi-calculus is a synchronous pi-calculus which is based on the SL model. The latter is a relaxation of the Esterel model where the reaction to the absence of a signal within an instant can only happen at the next instant. In the…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…