Ted's Codd Slogan for Normalization

1. “The key” : Tables may not contain repeating groups, which prevent a table from having a primary key. (1NF)
2. “the whole key”: Every attribute must be functionally dependent on the entire primary key. (2NF)
3. “and nothing but the key,” : There may not be any transitive dependencies, which involve a non-key field.(3NF)
4. “ so help me, Codd.” : The theorist who gave us these rules.

Codd produced these rules as part of a personal campaign to prevent his vision of the relational database being destroyed, as database vendors scrambled in the early 1980s to repackage existing products with a relational overlay. Rule 12 was particularly designed to counter such a positioning. Even if such re-packaged non-relational products eventually gave way to SQL DBMS, no popular relational database management systems are actually relational, be it by Codd's twelve rules or by the more formal definitions in his papers, in his books by its coworkers and successors, Christopher J. Date, David McGoveran and Fabian Pascal. Only less known DBMSs like Sybase strive to comply . The only commercial example, as of December 2010, is Dataphor. Some rules are controversial, especially rule three, because of the debate on three-valued logic.

This paper investigates the relationship between 'Three-valued logic' and 'Third Normal Form' in the context of database design and management. While these concepts are not directly related, both share a common theme in the quest for data consistency and accuracy. We will discuss their distinct roles and implications, delving into the importance of each concept in maintaining data integrity within relational databases.

The field of database management has given rise to various techniques and models aimed at optimizing the storage and retrieval of data. Among these, the concepts of 'Three-valued logic' and 'Third Normal Form' have garnered significant attention. Despite being distinct in nature and application, both share a common goal in ensuring data consistency and accuracy.

Three-valued logic (3VL) is a non-classical logic system that extends the traditional Boolean logic with a third truth value, typically represented as 'unknown' or 'null.' In classical Boolean logic, propositions can be evaluated as either true or false. However, in real-world scenarios, especially in database management, situations may arise where the truth value of a proposition cannot be determined. In such cases, three-valued logic provides a more nuanced approach, facilitating the representation of incomplete or missing information.
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value. This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for true and false. Conceptual form and basic ideas were initially created by Jan Lukasiewicz and C. I. Lewis. These were then re-formulated by Grigore Moisil in an axiomatic algebraic form, and also extended to n-valued logics in 1945.

Third Normal Form (3NF) is a database normalization technique aimed at eliminating data redundancy and ensuring data consistency in relational databases. This form, introduced by Edgar F. Codd in 1971, builds upon the principles of First and Second Normal Forms. A table is considered to be in 3NF if it meets the following criteria:

1. It is in Second Normal Form (2NF).
2. There are no transitive functional dependencies between non-prime attributes.

In simpler terms, 3NF ensures that all non-key attributes are fully dependent on the primary key, and there are no hidden relationships between non-key attributes that could lead to redundancy or inconsistency.

Upon examining the concepts of three-valued logic and third normal form, it becomes evident that these ideas are not directly related. However, they share a thematic connection in their pursuit of data consistency and accuracy.
Three-valued logic is particularly useful in database management when dealing with incomplete or uncertain data. By allowing the representation of 'unknown' or 'null' values, 3VL enables databases to store and process information that may be subject to change or further clarification. This contributes to the maintenance of data consistency and the accurate representation of real-world situations.
On the other hand, Third Normal Form focuses on eliminating redundancy and ensuring data consistency through the normalization process. By enforcing strict rules on the structure and relationships within a database, 3NF minimizes the chances of data anomalies and inaccuracies. Consequently, adherence to 3NF guarantees a higher degree of data integrity in relational databases.

While 'Three-valued logic' and 'Third Normal Form' are not directly related concepts, they share a common goal in promoting data consistency and accuracy. Three-valued logic provides a means to represent and process incomplete or uncertain information, whereas Third Normal Form eliminates redundancy and ensures data consistency through normalization. Both concepts play crucial roles in maintaining data integrity within relational databases, highlighting their significance in the broader context of database design and management.