Related papers: Rewriting Abstract Structures: Materialization Exp…
We describe a new method for summarizing similarities and differences in a pair of related documents using a graph representation for text. Concepts denoted by words, phrases, and proper names in the document are represented positionally as…
Automatic summarization is the process of shortening a set of textual data computationally, to create a subset (a summary) that represents the most important pieces of information in the original text. Existing summarization methods can be…
This paper addresses the following verification task: Given a graph transformation system and a class of initial graphs, can we guarantee (non-)reachability of a given other class of graphs that characterizes bad or erroneous states? Both…
We present a system for object recognition based on a semantic graph representation, which the system can learn from image examples. This graph is based on intrinsic properties of objects such as structure and geometry, so it is more robust…
A double category is constructed from a `fattened' version of a given category, motivated in part by a context of parallel transport. We also study monoidal structures on the underlying category and on the fattened category.
Equality saturation, a technique for program optimisation and reasoning, has gained attention due to the resurgence of equality graphs (e-graphs). E-graphs represent equivalence classes of terms under rewrite rules, enabling simultaneous…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
In this paper we investigate a ternary generalization of associativity by defining a diagrammatic calculus of hypergraphs that extends the usual notions of tensor networks, categories and relational algebras. In doing so we rediscover the…
Generating an abstract from a collection of documents is a desirable capability for many real-world applications. However, abstractive approaches to multi-document summarization have not been thoroughly investigated. This paper studies the…
We tackle the problem of attributed graph transformations and propose a new algorithmic approach for defining parallel graph transformations allowing overlaps. We start by introducing some abstract operations over graph structures. Then, we…
A categorical formalism for directed graphs is introduced, featuring natural notions of morphisms and subgraphs, and leading to two elementary descriptions of the free-properad monad, first in terms of presheaves on elementary graphs,…
This paper is dedicated to new methods of constructing weight structures and weight-exact localizations; our arguments generalize their bounded versions considered in previous papers of the authors. We start from a class of objects $P$ of…
In this paper we attempt to consider quantum superpositions from the perspective of the logos categorical approach presented in [26]. We will argue that our approach allows us not only to better visualize the structural features of quantum…
Learning abstractions directly from data is a core challenge in robotics. Humans naturally operate at an abstract level, reasoning over high-level subgoals while delegating execution to low-level motor skills -- an ability that enables…
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
Man-made 3D shapes are naturally organized in parts and hierarchies; such structures provide important constraints for shape reconstruction and generation. Modeling shape structures is difficult, because there can be multiple hierarchies…
The rewriting method for text summarization combines extractive and abstractive approaches, improving the conciseness and readability of extractive summaries using an abstractive model. Exiting rewriting systems take each extractive…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
Double-pushout rewriting is an established categorical approach to the rule-based transformation of graphs and graph-like objects. One of its standard results is the construction of concurrent rules and the Concurrency Theorem pertaining to…
Document Summarization is the procedure of generating a meaningful and concise summary of a given document with the inclusion of relevant and topic-important points. There are two approaches: one is picking up the most relevant statements…