# DATA ALGEBRA®

Permission is the Data Algebra Company: We make all data interoperable.

## What is data algebra®?

Data Algebra® applies various sets of theoretical operations and abstract algebra to database management and integration.

Data Algebra translates and transforms data from one form to another, providing access to databases and making different systems interrogatable and communicable in any format. Its capabilities include searching and retrieving structured and unstructured information available on any computer network.

Until its development, no complete means of representing and transforming data (and metadata) existed.

### All data is now liquid

Data Algebra can liquify any set of big data, then represent it in any form and map between equivalent data structures. It can treat a full set of personal data currently distributed in multiple locations as a single logical data store, allowing for unification and interoperability of all personal data.

Data Algebra enables data sourced from a variety of formats to be normalized. Now, data stored in any and all databases – Relational, Flat, JSON, XML, Blockchain, and more – can be integrated and queryable.

The ability to liquify data is fundamental to Permission’s mission. Individuals can now aggregate data from multiple sources (shopping, social, health, financial, etc) and monetize that data across the entire digital ecosystem. For advertisers, it enables a comprehensive understanding of an individual’s data, resulting in more meaningful engagement and increased ROI.

### Data Algebra® FAQS

What is Data Algebra?

It is a novel application of set theory, an algebra that can be applied to the representation and manipulation of data. It was invented and tested for database management and computer modeling.

Is Data Algebra like relational algebra?

They cannot be compared for several reasons, chief of which is that what is called “relational algebra” (created over 40 years ago by Edgar F. Codd while at IBM) is not mathematically sound and hence to call it an algebra is a misnomer. As such, “relational algebra” provides a means of manipulating data held in tabular, which, among other things, includes a set-theoretical anomaly (i.e. error): the null value. It has a limited area of application.

What is the basic “atom” of data?

In outline, Data Algebra could be described as follows: The basic unit of data is a two-term couplet, such as (a, b). A set of couplets is called a relation. A set of relations is called a clan. A set of clans is called a horde. For a detailed mathematical explanation of these structures and their operators, please read the book The Algebra of Data, By Sherman and Bloor, or download a PDF version from our web site.

What can Data Algebra be used for?

It can be used to represent any collection of data, and any part of that collection. It is complete in that there are no data structures that it cannot represent. In respect of software, it can, for example: be used to carry out any data transformation. (A data transformation is simply a reorganization of data from a source structure to a target structure.) be used for querying. (Mathematically, a query is simply a function that is applied to a data collection of some kind, selecting parts of it.) be used for data virtualization. be used for query optimization. In theory, it is not limited in its areas of application since Data Algebra could be applied in any context where data is manipulated.

Where has Data Algebra been applied?

Data Algebra has been applied to create, query, and manipulate the following data structures: Data caches and flat files; Key-value stores; Relational (i.e. table-based) databases; Document (i.e. noSQL) databases; XML databases; RDF (or triplestore) databases

Where is it currently in use?

Permission.io is currently applying Data Algebra in a large data integration project called Permission QE. The goal is to use the PartiQL query language to access datastores in multiple distributed locations so that personal data can be integrated and analyzed.