Re: compound propositions

paul c wrote:

> David BL wrote:
> ...
> 

sigh See ISO/IEC 2382 -- defined there.

I will start by directing you to the ISO/IEC 2382 standard vocabularies so that you will have the necessary grounding to understand the differences between conceptual, logical and physical as well as the definitive difference between information and data. The standard also defines internal and external. When I use these terms, I use the definions in ISO/IEC 2382.

Once you have done so, the remainder of this post will be redundant.

When I use terms like relation, predicate, extension etc. I use the common definitions in mathematics and in predicate logic particularly.

Conceptually, a relation is the extension of some predicate. A relation variable is the varying extension of some varying predicate. Most commonly, both predicate and extension vary with time.

Considering a simple example from business like inventory, the number of various items on hand depends on myriad factors: how many people called in sick at various businesses on various days, when and for how long various fabrication equipment broke down, labor disputes, customer demand, varying commodity prices etc.

Conceptually the predicate and its extension depend on all these factors; however, most of these factors are immeasurable and/or uninteresting. While all these past events conceptually create information that eventually determines inventory, they are not data. The information is not represented suitably for machine processing.

The myriad factors, many of which are never directly recorded anywhere, make the predicate unamenable to representing for machine processing. For our logical system, we choose instead to work directly with the extension of the predicate in relation form.

While the predicate overall may not be known, some properties of the predicate are. For example, the inventory on hand will never be negative. The relational algebra or the relational calculus allows us to describe some parts of the predicate using well-formed formulae. These parts of the predicate have a data representation amenable to machine processing. As such, they have a representation internal to our logical formalism. The rest of the predicate exists but only external to our formalism.

When expressed to a dbms, these representable parts of the predicate get represented internal to the dbms, and the rest of the predicate exists only external to the dbms. Within the scope of the dbms, the rest does not exist.

Thus, the internal predicate is that part of the predicate amenable to machine processing and actually expressed within some system. In general, internal predicate refers to those parts of the predicate available at the logical level of discourse. Predicate (unqualified) refers to the predicate at the conceptual level of discourse. External predicate refers to what's left of the predicate after one factors out internal predicate.

Other than a shorthand for "the parts we don't care about", the term external predicate is somewhat superfluous. Database constraints are the internal predicates of the relations in the database. As such, internal predicate is superfluous; although, it gives us a way to place and orient database constraints to the conceptual level of discourse. Received on Thu Mar 18 2010 - 19:14:31 CET