Olog

Olog is a knowledge representation language based on category theory, short for ontology log. It was developed to provide a diagrammatic and mathematically grounded way to model concepts and their relationships. An olog aims to capture how information is organized and how data from different sources relate to one another.

In an olog, the basic building blocks are types and relationships. Types are represented as boxes and denote classes of objects or concepts, such as Person, City, or Country. Relationships are arrows between types and describe functions or mappings, for example bornIn: Person -> City or locatedIn: City -> Country. Arrows are named with natural language phrases to make the diagram readable. Complex relationships are formed by composing arrows, and constraints can be expressed by equating different paths between types.

Semantics in an olog are explained by a simple model: each type corresponds to a set of its instances, and each arrow corresponds to a function between these sets. A diagram may include multiple paths from one type to another, and when different paths commute, the diagram enforces a consistency condition (a “fact”) within the model. This gives ologs a formal meaning while preserving intuitive diagrams.

Origins and use cases: ologs were introduced by researchers including David I. Spivak as a categorical framework for knowledge representation. They are used to illustrate how data and concepts can be organized in a way that supports reasoning, integration with external datasets, and translation between schemas in a principled manner. The approach has applications in education, data modeling, and knowledge-based systems.

See also: category theory, ontology, knowledge representation, database schemas. References include Spivak and colleagues’ work on ologs and their categorical foundations.