Related papers: Constructive Galois Connections
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field…
Girard's Geometry of Interaction (GoI), a semantics designed for linear logic proofs, has been also successfully applied to programming language semantics. One way is to use abstract machines that pass a token on a fixed graph along a path…
The introduction of separation logic has led to the development of symbolic execution techniques and tools that are (functionally) compositional with function specifications that can be used in broader calling contexts. Many of the…
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…
The functional correspondence is a manual derivation technique transforming higher-order evaluators into the semantically equivalent abstract machines. The transformation consists of two well-known program transformations: translation to…
Geometry of Interaction (GoI) is a kind of semantics of linear logic proofs that aims at accounting for the dynamical aspects of cut-elimination. We present here a parametrized construction of a Geometry of Interaction for Multiplicative…
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…
We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We…
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…
In this paper we focus on functions of the form $A^n\rightarrow \mathcal{P}(B)$, for possibly different arbitrary non-empty sets $A$ and $B$, and where $\mathcal{P}(B)$ denotes the set of all subsets of $B$. These mappings are called…
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…
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI.…
Explainable Artificial Intelligence (XAI) plays a crucial role in fostering transparency and trust in AI systems, where traditional XAI approaches typically offer one level of abstraction for explanations, often in the form of heatmaps…
This paper studies expansions of bounded distributive lattices equipped with a Galois connection. We introduce GC-frames and canonical frames for these algebras. The complex algebras of GC-frames are defined in terms of rough set…
The notion of Galois currents in Rational Conformal Field Theory is introduced and illustrated on simple examples. This leads to a natural partition of all theories into two classes, depending on the existence of a non-trivial Galois…
Geometric reasoning inherently requires "thinking with constructions" -- the dynamic manipulation of visual aids to bridge the gap between problem conditions and solutions. However, existing Multimodal Large Language Models (MLLMs) are…
Generalising the notion of Galois corings, Galois comodules were introduced as comodules $P$ over an $A$-coring $\cC$ for which $P_A$ is finitely generated and projective and the evaluation map $\mu_\cC:\Hom^\cC(P,\cC)\ot_SP\to \cC$ is an…
This paper concerns the development of metatheory for extensible languages. It uses as its starting point a view that programming languages tailored to specific application domains are to be constructed by composing components from an open…
ProbLog is a popular probabilistic logic programming language/tool, widely used for applications requiring to deal with inherent uncertainties in structured domains. In this paper we study connections between ProbLog and a variant of…