Ologs: a categorical framework for knowledge representation

Abstract

In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.

38 pages

References in corpus (3)

• Higher-dimensional models of networks
• Functorial Data Migration
• The IFF Approach to the Lattice of Theories

Cited by in corpus (20)

• Category theoretic analysis of hierarchical protein materials and social networks
• Reoccurring patterns in hierarchical protein materials and music: The power of analogies
• Operads for complex system design specification, analysis and synthesis
• Database queries and constraints via lifting problems
• Bitcoin: a Money-like Informational Commodity
• Knowledge Engineering for Wind Energy
• Teaching machines to understand data science code by semantic enrichment of dataflow graphs
• FOLE: The First-order Logical Environment
• Theories of anything
• PlanAlyzer: Assessing Threats to the Validity of Online Experiments
• Gene ologs: a categorical framework for Gene Ontology
• A Compositional Framework for Scientific Model Augmentation
• Applied Category Theory for Genomics -- An Initiative
• Data-Centric AI Requires Rethinking Data Notion
• Toward formalizing ologs: Linguistic structures, instantiations, and mappings
• The ERA of FOLE: Foundation
• A category-theoretic approach to modeling John Cage's Silent piece
• Mathematical modelling by help of category theory: models and relations between them
• Modelling Compositionality and Structure Dependence in Natural Language
• Categorical Data Integration for Computational Science