Related papers: Knowledge Representation in Bicategories of Relati…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
This paper proposes a categorical framework for knowledge graphs linking combinatorial graph structure with topos-theoretic semantics. Knowledge graphs are represented as labelled directed multigraphs and analysed through incidence matrices…
Retrieval-augmented generation (RAG) enhances large language models by grounding outputs in retrieved knowledge. However, existing RAG methods including graph- and hypergraph-based approaches treat retrieved evidence as an unordered set,…
This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…
Commonsense knowledge relations are crucial for advanced NLU tasks. We examine the learnability of such relations as represented in CONCEPTNET, taking into account their specific properties, which can make relation classification difficult:…
Knowledge representation learning (KRL) aims to represent entities and relations in knowledge graph in low-dimensional semantic space, which have been widely used in massive knowledge-driven tasks. In this article, we introduce the reader…
We show that the proof-theoretic notion of logical preorder coincides with the process-theoretic notion of contextual preorder for a CCS-like calculus obtained from the formula-as-process interpretation of a fragment of linear logic. The…
Subtyping, also known as subtype polymorphism, is a concept extensively studied in programming language theory, delineating the substitutability relation among datatypes. This property ensures that programs designed for supertype objects…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
We present a novel approach to knowledge graph visualization based on ontology design patterns. This approach relies on OPLa (Ontology Pattern Language) annotations and on a catalogue of visual frames, which are associated with foundational…
Ontologies contain rich knowledge within domain, which can be divided into two categories, namely extensional knowledge and intensional knowledge. Extensional knowledge provides information about the concrete instances that belong to…
Online behaviors of consumers and marketers generate massive marketing data, which ever more sophisticated models attempt to turn into insights and aid decisions by marketers. Yet, in making decisions human managers bring to bear marketing…
We present in this paper a reformulation of the usual set-theoretical semantics of the description logic $\mathcal{ALC}$ with general TBoxes by using categorical language. In this setting, $\mathcal{ALC}$ concepts are represented as…
In this paper we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
The usual modelling of the syllogisms of the Organon by a calculus of classes does not include relations. Aristotle may however have envisioned them in the first two books as the category of relatives, where he allowed them to compose with…
Knowledge graphs store large numbers of relations efficiently, but they remain weak at representing a quieter difficulty: the meaning of a concept often shifts with the domain in which it is used. A triple such as Apple, instance-of,…
Given a natural language phrase, relation linking aims to find a relation (predicate or property) from the underlying knowledge graph to match the phrase. It is very useful in many applications, such as natural language question answering,…
Natural language communication is an intricate and complex process. The speaker usually begins with an intention and motivation of what is to be communicated, and what effects are expected from the communication, while taking into…
Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In…