What are schemata

[Jarle Stabell]

Lars Marius Garshol wrote:

> * James K. Tauber
> |
> | So is a schema a function that maps a document to a truth value?
>
> I'd rather say that it is a definition of a set of documents, just as
> a formal language is usually considered to be the set of sentences
> that are well-formed in that language.
>
> The software that verifies a document could be called "a function that
> maps a document to a truth value", though. Mathematically, such
> software would perform an "element of"-test on the set of documents
> defined by the schema.

So by 'schema', you mean basically what is also known as 'type'? (I think I 
do)
The schema is the intension, the "recipe" of the set of "allowable" 
instances, while the set of "allowable" instances is it's extension.

In database theory, a schema (or is it also called 'scheme'?) defines the 
vocabulary you are allowed to build your "worlds" out of (the 
relation(ship)s/tables, and additionally constrains the set of "allowable 
worlds" (database instances/documents).
In mathematical logic, a sentence/formula is well-formed with respect to a 
language if it follows the syntactic rules of the given language (is a 
sentence in the language), but may state utter nonsense. It is valid if it 
is true no matter what the world looks like. (Valid if it is true 
irrespective of interpretation of the interpretable symbols)


Cheers,

Jarle Stabell
Digital Logikk AS


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