相关论文: Iteration Algebras for UnQL Graphs and Completenes…

We introduce a new method of expressing a $k$-graph $C^*$-algebra as a Cuntz-Pimsner algebra. Kumjian, Pask, and Sims have done this directly, using a linking algebra approach and a $(k-1)$-graph algebra. This can be iterated downward. Our…

The rise of Artificial Intelligence (AI) recently empowered researchers to investigate hard mathematical problems which eluded traditional approaches for decades. Yet, the use of AI in Universal Algebra (UA) -- one of the fields laying the…

Systematic discovery of optimization paths in quantum circuit simplification remains a challenge. Today, ZX-calculus, a computing model for quantum circuit transformation, is attracting attention for its highly abstract graph-based…

We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at…

Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…

Graph database has enjoyed a boom in the last decade, and graph queries accordingly gain a lot of attentions from both the academia and industry. We focus on analytical queries in this paper. While analyzing existing domain-specific…

Graph-based Retrieval-Augmented Generation (RAG) has proven effective in integrating external knowledge into large language models (LLMs), improving their factual accuracy, adaptability, interpretability, and trustworthiness. A number of…

Graph database systems are increasingly adapted for storing and processing heterogeneous network-like datasets. However, due to the novelty of such systems, no standard data model or query language has yet emerged. Consequently, migrating…

Large language models (LLMs) are being increasingly explored for graph tasks. Despite their remarkable success in text-based tasks, LLMs' capabilities in understanding explicit graph structures remain limited, particularly with large…

Significant efforts have been dedicated to integrating the powerful Large Language Models (LLMs) with diverse modalities, particularly focusing on the fusion of language, vision and audio data. However, the graph-structured data, which is…

Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…

Motivation: With the advent of Language Models using Transformers, popularized by ChatGPT, there is a renewed interest in exploring encoding procedures that numerically represent symbolic sequences at multiple scales and embedding…

Hierarchical graph rewriting is a highly expressive computational formalism that manipulates graphs enhanced with box structures for representing hierarchies. It has provided the foundations of various graph-based modeling tools, but the…

SQL/PGQ and GQL are very recent international standards for querying property graphs: SQL/PGQ specifies how to query relational representations of property graphs in SQL, while GQL is a standalone language for graph databases. The rapid…

We present DashQL, a language that describes complete analysis workflows in self-contained scripts. DashQL combines SQL, the grammar of relational database systems, with a grammar of graphics in a grammar of analytics. It supports preparing…

We define pure graphs, invertible graphs, and the notion of complementation of bicoloured graphs. The study of pure graphs is motivated by two conjectures about the transition systems of eulerian graphs and by the Cycle Double Cover…

Like [1], we present an algorithm to compute the simulation of a query pattern in a graph of labeled nodes and unlabeled edges. However, our algorithm works on a compressed graph grammar, instead of on the original graph. The speed-up of…

These notes present a compact and self-contained approach to iterated forcing with a particular emphasis on semiproper forcing. We tried to make our presentation accessible to any scholar who has some familiarity with forcing and boolean…

Graph query languages feature mainly two kinds of queries when applied to a graph database: those inspired by relational databases which return tables such as SELECT queries and those which return graphs such as CONSTRUCT queries in SPARQL.…

Querying knowledge bases using ontologies is usually performed using dedicated query languages, question-answering systems, or visual query editors for Knowledge Graphs. We propose a novel approach that enables users to query the knowledge…