Resumen
Knowledge and data representations are important for artificial intelligence (AI), as well as for intelligence in general. Intelligent functioning presupposes efficient operation with knowledge and data representations in particular. At the same time, it has been demonstrated that named sets, which are also called fundamental triads, instantiate the most fundamental structure in general and for knowledge and data representations in particular. In this context, named sets allow for effective mathematical portrayal of the key phenomenon, called nesting. Nesting plays a weighty role in a variety of fields, such as mathematics and computer science. Computing tools of AI include nested levels of parentheses in arithmetical expressions; different types of recursion; nesting of several levels of subroutines; nesting in recursive calls; multilevel nesting in information hiding; a variety of nested data structures, such as records, objects, and classes; and nested blocks of imperative source code, such as nested repeat-until clauses, while clauses, if clauses, etc. In this paper, different operations with nested named sets are constructed and their properties obtained, reflecting different attributes of nesting. An AI system receives information in the form of data and knowledge and processing information, performs operations with these data and knowledge. Thus, such a system needs various operations for these processes. Operations constructed in this paper perform processing of data and knowledge in the form of nested named sets. Knowing properties of these operations can help to optimize the processing of data and knowledge in AI systems.