Related papers: Constructive Galois Connections
Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory (inspired by ideas of Ernst…
We study properties that allow first-order theories to be disjointly combined, including stable infiniteness, shininess, strong politeness, and gentleness. Specifically, we describe a Galois connection between sets of decidable theories,…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
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…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
Rewriting logic is both a flexible semantic framework within which widely different concurrent systems can be naturally specified and a logical framework in which widely different logics can be specified. Maude programs are exactly rewrite…
Some conditions for the Galois map to be injective are given in the groupoid acting on a noncommutative ring context. In the particular case in which the Galois extension is a central Galois algebra, it is given a complete characterization…
In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…
Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…
Mechanized verification of liveness properties for infinite programs with effects and nondeterminism is challenging. Existing temporal reasoning frameworks operate at the level of models such as traces and automata. Reasoning happens at a…
Galois comodules of a coring are studied. The conditions for a simple comodule to be a Galois comodule are found. A special class of Galois comodules termed principal comodules is introduced. These are defined as Galois comodules that are…
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…
As modern computing moves towards smaller devices and powerful cloud platforms, more and more computation is being delegated to powerful service providers. Interactive proofs are a widely-used model to design efficient protocols for…
We present a framework for generating physically realizable assembly instructions from natural language descriptions. Unlike unconstrained text-to-3D approaches, our method operates within a discrete parts vocabulary, enforcing geometric…
Abstract separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
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,…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
We introduce Galois corings, and give a survey of properties that have been obtained so far. The Definition is motivated using descent theory, and we show that classical Galois theory, Hopf-Galois theory and coalgebra Galois theory can be…
Gradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. While existing gradual type soundness theorems for these languages aim to show that…