XIII Международная студенческая научная конференция Студенческий научный форум - 2021

Abstract: The article provides an overview of decisions made in the software development environment using three-digit logic, as well as ideas and works related to this topic. The analysis of the problems and the prospects of these solutions are carried out.

Keywords: three-digit logic, knowledge bases, logical programming, business processes.

The development of technologies in various fields of activity makes people use more complex intelligent systems of various directions. As you know, almost all information systems, as well as computers, use the binary number system to produce logic operations. But binary logic is not the best and only possible way to work with logic and has a number of disadvantages. The purpose of this paper is to consider examples of systems based on three-digit logic, work related to it, as well as problems and ways to solve them.

1. Three-Digit logic in SQL

In databases built on the third version of the query language SQL-92, for logical operations, in addition to the values of truth (true) and false (false), a new value is unknown (unknown). All logical operations in sql with an unknown value are based on the three-digit logic of Yan Lukasevich [1]. The problem with three-valued logic in query languages is that the value" unknown " is expressed in a single NULL value, and what exactly it means, is decided by the semantics of the subject area, which is not always convenient, and this gives rise to three cases of incomplete information: unknown, inapplicable, and possible.

C. J. Date writes about this, as well as about the solution of this problem, in his article [2]. The solution for Date is considered to be the introduction of an individual value for each case of incomplete information, which leads to the creation of a 5-digit logic. This article has its own critics, for example, Tom Johnson or Claude Rubinson. But at the moment, the SQL language has not changed and everything remains as before.

2. Logic programming and three-digit logic.

In logic programming, three-digit logic has found itself in building knowledge bases. The construction of such systems is described in detail in the work of I. A. Bessmertny [4]. The main idea of the thesis is the possibility of converting a partially binary knowledge base into a ternary one. A system for searching for a value in the database is also implemented, which takes into account the differences between the absence of a value and the lack of data to search for it.

This paper describes the problem of two-valued logic related to the closed world assumption (CWA), which implies that any statement that is not known to be true is false. In this regard, a search query in local databases for any resource will fail due to the lack of necessary facts that can be placed on other sources of information. To solve this problem, it is suggested to use the open world assumption (OWA), and also use the additional Boolean value "unknown". Also search in this intelligent system allows you to returnthe list of facts with credibility "0", and facts necessary for the reliability of the result that can be interpreted as: "the Result would be true if <Fact n>", which allows to distinguish the negation from the lack of information.

3. Three-Digit logic for Clearing and testing undefined data.

Three-digit logic is also used in testing. Article [6] describes testing algorithms in conditions of incomplete data this the use of three-digit logic, since the system can accept undefined states testing. It also suggest to use the types that support undefined values. The paper uses the term "refinement ratio", which allows you to compare the information content of values. A “refinement ratio” has a certain value in itself, and the larger it is, the more information this ratio carries.

Kleene's three-digit logic assumes that, when additional information is received, the Boolean value can only change from "undefined" to "true" or "false", but the value "true" cannot change to "false" and vice versa. For testing in conditions of incomplete information, the article uses 2 methods: "undefined

generalized models" and "generating tests based on undefined models". The latter, in turn, is divided into "graphs with clarifying vertices" and "algorithms for clarifying graph traversal".

References:

1. C. J. Date. A Critique of Claude Rubinson’s Paper Nulls, Three -

Valued Logic, and Ambiguity in SQL: Critiquing Date’s Critique. SIGMOD

Record, Vol. 37, No. 3, September 2008.

2. D.D. Chamberlin, M.M. Astrahan, K.P. Eswaran, P.P. Griffiths,

R.A. Gloria, J.W. Mehl, P. Reisner, B.W. Wade. SEQUEL 2: A Unified Approach to Data Definition, Manipulation, and Control. IBM Journal of Research and Development, V. 20, No. 6, 1976.

3. Corolla Y. A. Methods and means of constructing intellectual systems in ternary logic/ Koroleva Yu. a., Bessmertny I. A.-dissertation abstract, 2015

4. Claude Robinson. Nulls, Three-Valued Logic, and Ambiguity in

SQL: Critiquing Date’s Critique. SIGMOD Record, December 2007 (Vol. 36,

No. 4).

5. A. S. Kamkin. Testing in conditions of incomplete information.

Approach to the development of specifications and test generation/A. S. Kamkin-proceedings Of the Institute of system programming of the Russian Academy of Sciences.

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