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.
is a semigroup, representing combination or aggregation of information, and
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
, the following operations are defined Additionally, in
the usual lattice operations (meet and join) are defined.
The axioms of the two-sorted algebra
, in addition to the axioms of the lattice
combined with another information to domain
An information combined with a part of itself gives nothing new.
Each information refers to at least one domain (question).
satisfying these axioms is called an Information Algebra.
A partial order of information can be introduced by defining
a partial order can be introduced by defining
It represents the order of information content of
form a labeled Information Algebra.
More precisely, in the two-sorted algebra
, the following operations are defined Here follows an incomplete list of instances of information algebras: Let
be a set of symbols, called attributes (or column names).
is: A relational database with natural join
as combination and the usual projection
The operations are well defined since It is easy to see that relational databases satisfy the axioms of a labeled information algebra: The axioms for information algebras are derived from the axiom system proposed in (Shenoy and Shafer, 1990), see also (Shafer, 1991).