Related papers: Grammars Based on a Logic of Hypergraph Languages
Natural language generation systems (NLG) map non-linguistic representations into strings of words through a number of steps using intermediate representations of various levels of abstraction. Template based systems, by contrast, tend to…
Handling graph data is one of the most difficult tasks. Traditional techniques, such as those based on geometry and matrix factorization, rely on assumptions about the data relations that become inadequate when handling large and complex…
Large language models (LLMs) exhibit strong semantic understanding, yet struggle when user instructions involve ambiguous or conceptually misaligned terms. We propose the Language Graph Model (LGM) to enhance conceptual clarity by…
This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely…
The Int_reg-problem of a combinatorial problem P asks, given a nondeterministic automaton M as input, whether the language L(M) accepted by M contains any positive instance of the problem P. We consider the Int_reg-problem for a number of…
In this paper we study some fragments without implications of the (Hilbert) full Lambek logic $\mathbf{HFL}$ and also some fragments without implications of some of the substructural extensions of that logic. To do this, we perform an…
Unsupervised heterogeneous graph representation learning (UHGRL) has gained increasing attention due to its significance in handling practical graphs without labels. However, heterophily has been largely ignored, despite its ubiquitous…
In precision medicine, quantitative multi-omic features, topological context, and textual biological knowledge play vital roles in identifying disease-critical signaling pathways and targets. Existing pipelines capture only part of…
This paper introduces a model theory for resolution on Higher Order Hereditarily Harrop formulae (HOHH), the logic underlying the Lambda-Prolog programming language, and proves soundness and completeness of resolution. The semantics and the…
We introduce a correspondence principle (analogous to the Furstenberg correspondence principle) that allows one to extract an infinite random graph or hypergraph from a sequence of increasingly large deterministic graphs or hypergraphs. As…
Graph-based frames have been introduced as a logical framework which internalizes an inherent boundary to knowability. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential…
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…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
Knowledge Graphs (KGs) have long served as a fundamental infrastructure for structured knowledge representation and reasoning. With the advent of Large Language Models (LLMs), the construction of KGs has entered a new paradigm-shifting from…
Reasoning over knowledge graphs (KGs) with first-order logic (FOL) queries is challenging due to the inherent incompleteness of real-world KGs and the compositional complexity of logical query structures. Most existing methods rely on…
Large-scale natural language generation requires the integration of vast amounts of knowledge: lexical, grammatical, and conceptual. A robust generator must be able to operate well even when pieces of knowledge are missing. It must also be…
Existing technology can parse arbitrary context-free grammars, but only a single, static grammar per input. In order to support more powerful syntax-extension systems, we propose reflective grammars, which can modify their own syntax during…
Graph Retrieval-Augmented Generation (GraphRAG) has emerged as a promising paradigm that organizes external knowledge into structured graphs of entities and relations, enabling large language models (LLMs) to perform complex reasoning…
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…
Automatic extraction of procedural graphs from documents creates a low-cost way for users to easily understand a complex procedure by skimming visual graphs. Despite the progress in recent studies, it remains unanswered: whether the…