Postgresql – Is using multiple unique constrains on a single table considered bad design

Add a persisted computed column that combines the 18 keys, then create an unique index on the computed column:

alter table t add all_keys as c1+c2+c3+...+c18 persisted;
create unique index i18 on t (all_keys);

See Creating Indexes on Computed Columns.

Another approach is to create an indexed view:

create view v 
with schemabinding
as select c1+c2+c3+...+c18 as all_keys
from dbo.t;

create unique clustered index c18 on v(all_keys);

See Creating Indexed Views.

Both approaches allow for a partial key aggregate: aggregate c1+c2+c3 as k1, c4+c5+c6 as k2 etc. then index/create indexed view on (k1, k2, ...). Thia could be beneficial for range scans (index can be used for search on c1+c2+c3.

Of course, all + operation in my example are string aggregation, the actual operator to use depends on the types of all those columns (ie. you may have to use explicit casts).

PS. As unique constraints are enforced by an unique index, any restriction on unique indexes will apply to unique constraints as well:

create table t (
    c1 char(3), c2 char(3), c3 char(3), c4 char(3),
    c5 char(3), c6 char(3), c7 char(3), c8 char(3),
    c9 char(3), c10 char(3), c11 char(3), c12 char(3),
    c13 char(3), c14 char(3), c15 char(3), c16 char(3),
    c17 char(3), c18 char(3), c19 char(3), c20 char(3),
    constraint unq unique
      (c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15,c16,c17,c18));
go  


Msg 1904, Level 16, State 1, Line 3
The index '' on table 't' has 18 column names in index key list. 
The maximum limit for index or statistics key column list is 16.
Msg 1750, Level 16, State 0, Line 3
Could not create constraint. See previous errors.

However, creating the constraint on a persisted computed column works:

create table t (
    c1 char(3), c2 char(3), c3 char(3), c4 char(3),
    c5 char(3), c6 char(3), c7 char(3), c8 char(3),
    c9 char(3), c10 char(3), c11 char(3), c12 char(3),
    c13 char(3), c14 char(3), c15 char(3), c16 char(3),
    c17 char(3), c18 char(3), c19 char(3), c20 char(3),
    all_c as 
        c1+c2+c3+c4+c5+c6+c7+c8+c9+c10+c11+
        c12+c13+c14+c15+c16+c17+c18 
        persisted
        constraint unq unique (all_c));
go  

Obviously, the persisted column consumes the space on disk so the approach may be bad for a very large table. The indexed view approach does not have this problem, it only consumes the space for the index, not the space for the computed column and index.

There are a few problems with your tables. I'll try to address the foreign keys first, since you question asked about them :)

But before that, we should realize that the two sets of tables (the first three you created and the second set, which you created after dropping the first set) are the same. Of course, the definition of Table3 in your second attempt has syntax and logical errors, but the basic idea is:

CREATE TABLE table3 (   
  "ID" bigint NOT NULL DEFAULT '0',   
  "DataID" bigint DEFAULT NULL,   
  "Address" numeric(20) DEFAULT NULL,   
  "Data" bigint DEFAULT NULL,
   PRIMARY KEY ("ID"),   
   FOREIGN KEY ("DataID") REFERENCES Table1("DataID") on delete cascade on update cascade,   
   FOREIGN KEY ("Address") REFERENCES Table2("Address") on delete cascade on update cascade
);

This definition tell PostgreSQL roughly the following: "Create a table with four columns, one will be the primary key (PK), the others can be NULL. If a new row is inserted, check DataID and Address: if they contain a non-NULL value (say 27856), then check Table1 for DataID˙and Table2 for Address. If there is no such value in those tables, then return an error." This last point which you've seen first:

ERROR: insert or update on table "Table3" violates foreign key constraint 
    "Table3_DataID_fkey" DETAIL: Key (DataID)=(27856) is not present in table "Table1".

So simple: if there is no row in Table1 where DataID = 27856, then you can't insert that row into Table3.

If you need that row, you should first insert a row into Table1 with DataID = 27856, and only then try to insert into Table3. If this seems to you not what you want, please describe in a few sentences what you want to achieve, and we can help with a good design.

And now about the other problems.

You define your PKs as

CREATE all_your_tables (
    first_column NOT NULL DEFAULT '0',   
    [...]
    PRIMARY KEY ("ID"),  

A primary key means that all the items in it are different from each other, that is, the values are UNIQUE. If you give a static DEFAULT (like '0') to a UNIQUE column, you will experience bad surprises all the time. This is what you got in your third error message.

Furthermore, '0' means a text string, but not a number (bigint or numeric in your case). Use simply 0 instead (or don't use it at all, as I written above).

And a last point (I may be wrong here): in Table2, your Address field is set to numeric(20). At the same time, it is the PK of the table. The column name and the data type suggests that this address can change in the future. If this is true, than it is a very bad choice for a PK. Think about the following scenario: you have an address '1234567890454', which has a child in Table3 like

ID        DataID           Address             Data
123       3216547          1234567890454       654897564134569

Now that address happens to change to something other. How do you make your child row in Table3 follow its parent to the new address? (There are solutions for this, but can cause much confusion.) If this is your case, add an ID column to your table, which will not contain any information from the real world, it will simply serve as an identification value (that is, ID) for an address.