Related papers: Expressive Power of Hypergraph Lambek Grammars
Word-representable graphs, which are the same as semi-transitively orientable graphs, generalize several fundamental classes of graphs. In this paper we propose a novel approach to study word-representability of graphs using a technique of…
Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. Recent work at the intersection of formal language theory and graph theory has found that a Hyperedge Replacement Grammar (HRG)…
Large language models (LLMs) have achieved remarkable performance in natural language understanding and generation tasks. However, they often suffer from limitations such as difficulty in incorporating new knowledge, generating…
We describe two formalisms for defining graph languages, and prove that they are equivalent: 1. Separator logic. This is first-order logic on graphs which is allowed to use the edge relation, and for every $n \in \{0,1,\ldots \}$ a relation…
In this paper, firstly, we introduce a higher-dimensional analogue of hypergraphs, namely $\omega$-hypergraphs. This notion is thoroughly flexible because unlike ordinary $\omega$-graphs, an n-dimensional edge called an n-cell has many…
In addition to their limpid interface with semantics, categorial grammars enjoy another important property: learnability. This was first noticed by Buskowsky and Penn and further studied by Kanazawa, for Bar-Hillel categorial grammars. What…
Do current large language models (LLMs) better solve graph reasoning and generation tasks with parameter updates? In this paper, we propose InstructGraph, a framework that empowers LLMs with the abilities of graph reasoning and generation…
The article continues our study of the genus of a regular language $L$, defined as the minimal genus among all genera of all finite deterministic automata recognizing $L$. Here we define and study two closely related tools on a directed…
Large Language Models (LLMs) have demonstrated remarkable in-context learning capabilities, enabling flexible utilization of limited historical information to play pivotal roles in reasoning, problem-solving, and complex pattern recognition…
This paper introduces DW-Bench, a new benchmark that evaluates large language models (LLMs) on graph-topology reasoning over data warehouse schemas, explicitly integrating both foreign-key (FK) and data-lineage edges. The benchmark…
Goal-conditioned hierarchical reinforcement learning (HRL) decomposes complex reaching tasks into a sequence of simple subgoal-conditioned tasks, showing significant promise for addressing long-horizon planning in large-scale environments.…
We introduce the 2-sorted counting logic $GC^k$ that expresses properties of hypergraphs. This logic has available k variables to address hyperedges, an unbounded number of variables to address vertices, and atomic formulas E(e,v) to…
We introduce L-drawings, a novel paradigm for representing directed graphs aiming at combining the readability features of orthogonal drawings with the expressive power of matrix representations. In an L-drawing, vertices have exclusive…
Hypergraphs are higher-order networks that capture the interactions between two or more nodes. Hypergraphs can always be represented by factor graphs, i.e. bipartite networks between nodes and factor nodes (representing groups of nodes).…
Large language models (LLMs) have demonstrated immense potential across various tasks. However, research for exploring and improving the capabilities of LLMs in interpreting graph structures remains limited. To address this gap, we conduct…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…
Large Language Models (LLMs) have demonstrated remarkable generalization and instruction-following capabilities with instruction tuning. The advancements in LLMs and instruction tuning have led to the development of Large Vision-Language…
Graph neural networks have recently achieved remarkable success in representing graph-structured data, with rapid progress in both the node embedding and graph pooling methods. Yet, they mostly focus on capturing information from the nodes…
We consider tensor grammars, which are an example of \commutative" grammars, based on the classical (rather than intuitionistic) linear logic. They can be seen as a surface representation of abstract categorial grammars ACG in the sense…
Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…