The term "information algebra" refers to mathematical techniques of information processing. Classical information theory goes back to Claude Shannon. It is a theory of information transmission, looking at communication and storage. However, it has not been considered so far that information comes from different sources and that it is therefore usually combined. It has furthermore been neglected in classical information theory that one wants to extract those parts out of a piece of information that are relevant to specific questions.

A mathematical phrasing of these operations leads to an algebra of information, describing basic modes of information processing. Such an algebra involves several formalisms of computer science, which seem to be different on the surface: relational databases, multiple systems of formal logic or numerical problems of linear algebra. It allows the development of generic procedures of information processing and thus a unification of basic methods of computer science, in particular of distributed information processing.

Information relates to precise questions, comes from different sources, must be aggregated, and can be focused on questions of interest. Starting from these considerations, information algebras (Kohlas 2003) are two-sorted algebras ${\displaystyle (\Phi ,D)}$:

Where ${\displaystyle \Phi }$ is a semigroup, representing combination or aggregation of information, and

${\displaystyle D}$ is a lattice of domains (related to questions) whose partial order reflects the granularity of the domain or the question, and a mixed operation representing focusing or extraction of information.

More precisely, in the two-sorted algebra ${\displaystyle (\Phi ,D)}$, the following operations are defined

Additionally, in ${\displaystyle D}$ the usual lattice operations (meet and join) are defined.

The axioms of the two-sorted algebra ${\displaystyle (\Phi ,D)}$, in addition to the axioms of the lattice ${\displaystyle D}$: