As for making databases more intelligent, NTA can be considered an extension of relational algebra to knowledge processing. Besides, we propose an approach to development of search engines, in particular, question-and-answer teaching systems based on controlled languages and algebraic models for representation and processing of question-and-answer texts.
Science is organized knowledge. – Immanuel Kant
TopRelational Databases
In relational DBs, basic controlled objects are files organized in the form of tables (relations), which consist of a set of elementary tuples. In NTA terms, any table is representable as a C-system where all components are singletons. In other words, such C-systems comprise only elementary tuples. For instance, the table can be represented as the C-system P[XYZ] = 
:
This correspondence allows to use all database management tools including methods of searching by a key based on the theory of normal forms. However, it does not consider specific characteristics and benefits of NTA structures, in particular, their feature of using set components together with elementary ones. In intelligent systems, there dominate structures modeled by NTA objects with multi-element components: networks, inference rules, predicates, etc. Due to representing heterogeneous data and knowledge structures in the form of NTA objects, we achieved unification of their processing and acceleration of associated computational procedures.
In big data and knowledge systems, expressing relations as NTA objects provides more effective search for information, if these structures are processed in computer systems with a specific architecture discussed in Chapter 5, Techniques to Parallel NTA Algorithms, by means of associative search methods.
To perform operations with relations expressed in the form of database tables, relational algebra (RA) is used (Codd, 1970; Date, 1984). It supports a set of specific operations; six of them are basic: projection, union, intersection, direct product (Cartesian product), difference and selection. Other RA operations are implemented as combinations of basic ones. Let us show how to express the basic RA operations in NTA.
Consider the operation of projection. Let X and Y be sets of attributes and Y ⊂ X. In RA, the projection operation creates a relation Qp[Y] from the relation Q[X] by removing the columns with attributes of the set X \ Y and possible repeated identical tuples obtained in the resulting relation. In NTA, this operation corresponds to elimination of the attributes contained in the set X \ Y provided that Q[X] is expressed as a C-system.
The RA union operation is equivalent to the NTA union of C-systems with the same relation diagrams. Such an operation results in addition of all tuples from the second relation to the tuples from the first relation.
The RA intersection operation corresponds to the ordinary intersection of NTA objects modeling the initial relations.