Related papers: A Structural and Nominal Syntax for Diagrams
Construction Grammar (CxG) is a paradigm from cognitive linguistics emphasising the connection between syntax and semantics. Rather than rules that operate on lexical items, it posits constructions as the central building blocks of…
This paper delivers a new perspective of thinking and utilizing syntactic n-grams (sn-grams). Sn-grams are a type of non-linear n-grams which have been playing a critical role in many NLP tasks. Introducing sn-grams to comparing document…
The short note describes the chart parser for multimodal type-logical grammars which has been developed in conjunction with the type-logical treebank for French. The chart parser presents an incomplete but fast implementation of proof…
The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a lambda-calculus. Modal (boxed) types are intuitively interpreted as `closed syntax of the calculus'. This lambda-calculus is called modal type theory ---…
Knowledge Graphs, such as Wikidata, comprise structural and textual knowledge in order to represent knowledge. For each of the two modalities dedicated approaches for graph embedding and language models learn patterns that allow for…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…
In fields ranging from business to systems biology, directed graphs with edges labeled by signs are used to model systems in a simple way: the nodes represent entities of some sort, and an edge indicates that one entity directly affects…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
Domain specific languages (DSLs) are increasingly used today. Coping with complex language definitions, evolving them in a structured way, and ensuring their error freeness are the main challenges of DSL design and implementation. The use…
Multi-word expressions, verb-particle constructions, idiomatically combining phrases, and phrasal idioms have something in common: not all of their elements contribute to the argument structure of the predicate implicated by the expression.…
Checking consistency between an object diagram (OD) and a class diagram (CD) is an important analysis problem. However, several variations in the semantics of CDs and ODs, as used in different contexts and for different purposes, create a…
Multimodal UI design and development tools that interpret sketches or natural language descriptions of UIs inherently have notations: the inputs they can understand. In AI-based systems, notations are implicitly defined by the data used to…
Graphical languages are symmetric monoidal categories presented by generators and equations. The string diagrams notation allows to transform numerous axioms into low dimension topological rules we are comfortable with as three dimensional…
One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…
While numerous attempts have been made to jointly parse syntax and semantics, high performance in one domain typically comes at the price of performance in the other. This trade-off contradicts the large body of research focusing on the…
Bigraphs are an emerging modeling formalism for structures in ubiquitous computing. Besides an algebraic notation, which can be adopted to provide an algebraic syntax for bigraphs, the bigraphical theory introduces a visual concrete syntax…
The task of constructing compositional semantics for network-style diagrammatic languages, such as electrical circuits or chemical reaction networks, has been dubbed the black boxing problem, as it gives semantics that describes the…
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…
Wiring diagrams, as seen in digital circuits, can be nested hierarchically and thus have an aspect of self-similarity. We show that wiring diagrams form the morphisms of an operad $\mcT$, capturing this self-similarity. We discuss the…
Formal grammars are extensively used in Computer Science and related fields to study the rules which govern production of a language. The use of these grammars can be extended beyond mere language production. One possibility is to view…