相关论文: Transforming structures by set interpretations

Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format. While the existing notions are well-investigated concerning expressiveness, they all lack a proper notion of…

We describe two ``semantically-oriented'' dependency-structure formalisms, U-forms and S-forms. U-forms have been previously used in machine translation as interlingual representations, but without being provided with a formal…

Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of omega-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is…

In the context of structure-to-structure transformation tasks, learning sequences of discrete symbolic operations poses significant challenges due to their non-differentiability. To facilitate the learning of these symbolic sequences, we…

This paper studies the logical properties of a very general class of infinite ranked trees, namely those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal mu-calculus, three main…

Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and…

We prove that the MSO+U logic is compositional in the following sense: whether an MSO+U formula holds in a tree T depends only on MSO+U-definable properties of the root of T and of subtrees of T starting directly below the root. Another…

The underlying structure of natural language is hierarchical; words combine into phrases, which in turn form clauses. An awareness of this hierarchical structure can aid machine learning models in performing many linguistic tasks. However,…

Extending G\"odel's \emph{Dialectica} interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite…

We propose a novel interpretation technique to explain the behavior of structured output models, which learn mappings between an input vector to a set of output variables simultaneously. Because of the complex relationship between the…

An important factor in the practical implementation of optimization models is the acceptance by the intended users. This is influenced among other factors by the interpretability of the solution process. Decision rules that meet this…

We establish that the bisimulation invariant fragment of MSO over finite transition systems is expressively equivalent over finite transition systems to modal mu-calculus, a question that had remained open for several decades. The proof…

We propose terminology to classify interpretations of quantum mechanics and models that modify or complete quantum mechanics. Our focus is on models which have previously been referred to as superdeterministic (strong or weak), retrocausal…

Probabilistic sentential decision diagrams are a class of structured-decomposable probabilistic circuits especially designed to embed logical constraints. To adapt the classical LearnSPN scheme to learn the structure of these models, we…

We investigate the decidability of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N};<,P_1, \ldots,P_d \rangle$, for various unary predicates $P_1,\ldots,P_d \subseteq \mathbb{N}$. We focus in particular on…

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…

This work introduces a novel interpretable machine learning method called Mixture of Decision Trees (MoDT). It constitutes a special case of the Mixture of Experts ensemble architecture, which utilizes a linear model as gating function and…

The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…

Deep Learning models enjoy considerable success in Natural Language Processing. While deep architectures produce useful representations that lead to improvements in various tasks, they are often difficult to interpret. This makes the…

Model transformation tools assist system designers by reducing the labor--intensive task of creating and updating models of various aspects of systems, ensuring that modeling assumptions remain consistent across every model of a system, and…