Related papers: Hypergraph Lambek Calculus

In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…

Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. While graph learning has achieved remarkable progress, real-world graph data presents…

Graph neural networks (GNNs) have become a standard paradigm for graph representation learning, yet their message passing mechanism implicitly assumes that messages can be represented by source node embeddings, an assumption that fails in…

Large language models (LLMs), such as GPT4 and LLaMA, are creating significant advancements in natural language processing, due to their strong text encoding/decoding ability and newly found emergent capability (e.g., reasoning). While LLMs…

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…

Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes,…

Large Language Models (LLMs) have gained the ability to assimilate human knowledge and facilitate natural language interactions with both humans and other LLMs. However, despite their impressive achievements, LLMs have not made significant…

Integrating large language models (LLMs) with knowledge graphs derived from domain-specific data represents an important advancement towards more powerful and factual reasoning. As these models grow more capable, it is crucial to enable…

We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof…

There are many open questions surrounding the characterisation of groups with context-sensitive word problem. Only in 2018 was it shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is…

In graph signal processing, learning the weighted connections between nodes from a set of sample signals is a fundamental task when the underlying relationships are not known a priori. This task is typically addressed by finding a graph…

We enrich the Lambek calculus with the cyclic shift operation, which is expected to model the closure operator of formal languages with respect to cyclic shifts. We introduce a Gentzen-style calculus and prove cut elimination. Secondly, we…

Graphs are increasingly becoming ubiquitous as models for structured data. A generative model that closely mimics the structural properties of a given set of graphs has utility in a variety of domains. Much of the existing work require that…

Multi-step retrieval-augmented generation (RAG) has become a widely adopted strategy for enhancing large language models (LLMs) on tasks that demand global comprehension and intensive reasoning. Although many RAG systems incorporate a…

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…

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…

Despite the superior performance of large language models to generate natural language texts, it is hard to generate texts with correct logic according to a given task, due to the difficulties for neural models to capture implied rules from…

For large language models (LLMs), reasoning over graphs could help solve many problems. Prior work has tried to improve LLM graph reasoning by examining how best to serialize graphs as text and by combining GNNs and LLMs. However, the…

We present a translation of the Lambek calculus with brackets and the unit constant, $\mathbf{Lb}^{\boldsymbol{*}}_{\mathbf{1}}$, into the Lambek calculus with brackets allowing empty antecedents, but without the unit constant,…

Integrating knowledge graphs (KGs) to enhance the reasoning capabilities of large language models (LLMs) is an emerging research challenge in claim verification. While KGs provide structured, semantically rich representations well-suited…