What is a Theory?
Inspired by the article, What is a Knowledge Graph?; I am writing this blog post to explain the difference between a graph, knowledge graph, an ontology, a schema, a theory, and a system.
Network theory is part of graph theory. A graph is a mathematical structure used to explain relationships between objects. A graph, in formal graph theory jargon, is made up of vertices and edges. As I pointed out in Financial Report Knowledge Graphs (section 1.4, page 10), the terms "vertices" and "edge" are very precise technical terms which have more common aliases including:
- Vertices (vertex): Node, Point, Entity, Thing, Report Element
- Edge: Relationship, Line, Path, Association
The terms "graph" and "network" are sometimes used interchangeably. But to be precise, a graph is an abstract mathematical structure and a network is a real-world system instantiation of a graph.
A knowledge graph, is a graph (i.e. vertices and edges) that explains how and why they are connected. A graph is like a map. A knowledge graph is the actual territory that is explained by the map.
Another analogy is to think of a graph as the blueprint of a city which shows the intersections and roads of the city drawn abstractly. A network is the actual city itself with traffic, road signs, traffic lights, speed limits, and people moving through the intersections and roads.
A knowledge graph captures the meaning (i.e. the semantics) of the network in the form of a graph of vertices and edges. That graph of knowledge or knowledge graph is not random or haphazard. A good knowledge graph is deliberate, rigorous, and intentional. To best describe that real-world network, the knowledge graph needs to be complete. The knowledge graph must be clear.
A part of that knowledge graph is an ontology. An ontology is a formal description of the vertices or "things" in the knowledge graph and the edges or "relations between those things".
But all the rules needed cannot be described by an ontology alone. There are conditions that an ontology cannot explain. Additional assertions, restrictions, constraints, and other required conditions that need to be described can be described within a schema of the knowledge graph.
While an ontology describes the things and their relations; a schema describes the structure of a knowledge graph. Also, ontologies tend to be general in nature and not system specific; ontologies excel at cross system explanations. Schemas tend to be specific to a system.
Further, neither ontologies nor schemas tend to be designed for enforcing mathematical relationships; if you have a system that is number intensive, such as accounting, you need a mechanism that is good in that area. For XBRL that mechanism is XBRL Formula and its forthcoming successor, the XBRL Query and Rules Language.
To fend off the threat of inaccuracy within a knowledge graph you need more than just an ontology. You do need an ontology; but you also need a schema and you might need a few other things. The most powerful tool for representing what might be referred to as a conceptual model is the theory.
A system can be explained using a theory. A theory is an abstract conceptualization of specific important details of the nature and structure of some system which relates to some area of knowledge. The theory provides a way of thinking about the system.
As is pointed out in that first article I referenced, What is a Knowledge Graph?, "a knowledge graph is a web of meaning - and in a world where intelligence becomes cheap, meaning is set to become everything."
Saying this another way, a system is a set of interrelated and interdependent elements (a.k.a. parts, things), groups (a.k.a. types, categories, sets) into which the elements fall, and interaction patterns that describe the interactions between the different types of elements within a system which has purpose. A system has a nature and structures. Systems can be described using knowledge graphs; preferably global open standards based representation mechanisms.
Bill Gates coined the phrase, "Content is king," back in 1996. I believe Bill Gates got it right. A knowledge graph is content. That content will be created by talented, skilled, and experienced subject matter experts in specific areas of knowledge. There is exactly ZERO probability that machine learning or any other probability based artificial intelligence can generate a graph of knowledge that correctly explains an area of knowledge such as accountancy. ZERO.
However; after that quality knowledge graph exists; then probability based artificial intelligence will have a field day adding value to that base set of information provided within a knowledge graph.
Software that empowers those talented, skilled, experienced subject matter experts will be priceless. But what is the value of that software without the high quality knowledge graph that drives that software?
Humans are underrated. Much of AI is hype. That said, artificial intelligence, both rules-based and probability-based has a lot to offer. I predict that software will be built on top of machine interpretable theories.
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