Related papers: Grammars Based on a Logic of Hypergraph Languages

An enormous amount of real-world data exists in the form of graphs. Oftentimes, interesting patterns that describe the complex dynamics of these graphs are captured in the form of frequently reoccurring substructures. Recent work at the…

Random hypergraphs extend the classical notion of random graphs by allowing hyperedges to join more than two vertices, making them well-suited for modeling higher-order interactions in complex systems. Despite their broad applicability,…

In this paper, we investigate the retrieval-augmented generation (RAG) based on Knowledge Graphs (KGs) to improve the accuracy and reliability of Large Language Models (LLMs). Recent approaches suffer from insufficient and repetitive…

Context-Free Grammars (CFGs) and Parsing Expression Grammars (PEGs) have several similarities and a few differences in both their syntax and semantics, but they are usually presented through formalisms that hinder a proper comparison. In…

Given that substantial amounts of domain-specific knowledge are stored in structured formats, such as web data organized through HTML, Large Language Models (LLMs) are expected to fully comprehend this structured information to broaden…

In formal language theory, one of the most fundamental tools, known as pumping lemmas, is extremely useful for regular and context-free languages. However, there are natural properties for which the pumping lemmas are of little use. One of…

For any context-free grammar, we build a transition diagram, that is, a finite directed graph with labeled arcs, which describes the work of the grammar. This approach is new, and it is different from previously known graph models. We…

Large language models (LLMs) often suffer from hallucination, generating factually incorrect statements when handling questions beyond their knowledge and perception. Retrieval-augmented generation (RAG) addresses this by retrieving…

Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…

We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…

We present new descriptive complexity characterisations of classes REG (regular languages), LCFL (linear context-free languages) and CFL (context-free languages) as restrictions on inference rules, size of formulae and permitted connectives…

Graph retrieval-augmented generation (GraphRAG) has emerged as a powerful paradigm for enhancing large language models (LLMs) with external knowledge. It leverages graphs to model the hierarchical structure between specific concepts,…

A graph is a fundamental data model to represent various entities and their complex relationships in society and nature, such as social networks, transportation networks, and financial networks. Recently, large language models (LLMs) have…

Large language models (LLMs) are increasingly used for text-rich graph machine learning tasks such as node classification in high-impact domains like fraud detection and recommendation systems. Yet, despite a surge of interest, the field…

In this work, we introduce a new notion for representing graph classes with formal languages. In contrast to the seminal work by Kitaev and Pyatkin to represent graphs by words, we use formal binary languages in order to have a set of…

Retrieval-augmented generation (RAG) empowers large language models to access external and private corpus, enabling factually consistent responses in specific domains. By exploiting the inherent structure of the corpus, graph-based RAG…

Large language models (LLMs) have achieved remarkable success and demonstrated superior performance across various tasks, including natural language processing (NLP), weather forecasting, biological protein folding, text generation, and…

We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an…

Large Language Models (LLMs) exhibit persistent logical failures in complex reasoning due to the lack of an internal axiomatic framework. We propose Mathesis, a neuro-symbolic architecture that encodes mathematical states as higher-order…

Multilinear Grammar provides a framework for integrating the many different syntagmatic structures of language into a coherent semiotically based Rank Interpretation Architecture, with default linear grammars at each rank. The architecture…