Re: Conceptual model based on set theory

According to (3) from my previous post and with the application of set theory, we get the decomposition on the binary structures:

{Ie1, A11, A21, ..., An1} = {Ie1, A11} U {Ie1, A21} U ... U {Ie1, An1}
Where Ie1 is the name of the identifier of entity E11. A11, A21,..., An1 are names of attributes of Entity E11.

We can use the following K. Kuratowski's definition of the ordered pair: (a,b) = {{a}, {a,b}}

In my paper, from may 2006 at Definition 4.1, I introduced "Simple Form". Relation schema R (Ie, A1, A2,...,An) is in Simple Form if R satisfies:

R (Ie, A1, A2, ...,An) = R1 (Ie, A1) join R2 (Ie, A2), join ... join Rn (Ie, An)
 if and only if

1. Key Ie is simple
2. A1, A2,... , An are mutually independent.

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   The relationship between E11 = {Ie1, A11, A21, ..., An1}and E12 = {Ie2, A12, A22, ..., An2} is R12 = {Ir, Ie1, Ie2, A1, A2, ... Ak}. Ir is the name of the identifier of R12. Ie1 is the name of the identifier of E11. Ie2 is the name of the identifier of E12. A1, A2, ..., An are names of attributes of the relationship. Now in a manner similar to entities, we can obtain the decomposition into binary structure, but now, for relationships:
   {Ir, Ie1, Ie2, A1, A2, ... Ak} = {Ir, Ie1} U {Ir, Ie2} U {Ir, A1} U {Ir, A2}
   U ... U {Ir, Ak}

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In a similar way we can obtain conceptual model for states of entities and for states of relationships. I mean the conceptual model based on set theory.

Vladimir Odrljin Received on Wed Jul 29 2015 - 10:35:57 CEST