Applying simple theory of types to data bases

What is it about?

Whereas the logical apparatus used for formulation and solution of problems connected with the data base systems is mostly a 1st order logic, here a modified version (“T-system”) of Church's simple theory of types is used. It is shown that the T-system (a) is a more adequate tool for analyzing natural language, which may be important when one builds up an abstract model of a fragment of reality and when one creates a suitable philosophy of data base systems; (b) has greater expressive power than the 1st order systems, which enables, e.g. to distinguish between queries according to what is the structure of the required answer, and moreover, not to be restricted by the well-known limitations of the 1st order logics; (c) is based on the notion of function as on the most fundamental notion, which makes it possible to deal more directly with functional dependencies and to exploit more universally the key importance of the attribute concept; (d) by using the concept of construction offers a good tool for E-C mapping and for forming query languages that are more universal than the current ones. The analysis of these properties of the T-system is accompanied by examples from the area of the data base systems theories; especially, a comparison with Codd's domain relational calculus and with Chen's and Pirotte's approaches is made. No problem of implementation is touched in this paper.

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