universe-of-discourse

See also

object-creation | theory-derivation

Definition

A universe-of-discourse is a (possibly empty) collection of objects.

\[\left( o_1, o_2, \ldots, o_n \right)\]

Where:

• \(o_i\) is an object

If we organize objects in (desirably mutually exclusive but necessarily exhaustive) categories 1 , a universe-of-discourse is equivalently defined as a tuple:

\[\left( \mathcal{C}_1, \mathcal{C}_2, \ldots, \mathcal{C}_n \right)\]

Where:

• \(\mathcal{C}_i\) is an object category.

Considering the set of mutually exclusive and exhaustive object categories implemented by punctilious, a universe-of-discourse is equivalently defined as a tuple:

\[\left( \mathcal{I}, \mathcal{A}, \mathcal{D}, \mathcal{O}, \mathcal{R}, \mathcal{\Phi}, \mathcal{T} \right)\]

Where:

• \(\mathcal{I}\) is a (possibly empty) collection of inference-rule declarations

• \(\mathcal{A}\) is a (possibly empty) collection of axiom declarations

• \(\mathcal{D}\) is a (possibly empty) collection of definition declarations

• \(\mathcal{O}\) is a (possibly empty) collection of simple object declarations

• \(\mathcal{R}\) is a (possibly empty) collection of connective declarations

• \(\mathcal{\Phi}\) is a (possibly empty) collection of formulae declarations

• \(\mathcal{T}\) is a (possibly empty) collection of theory declarations

Note

The lifecycle of objects

For objects (including universes-of-discourse) to exist, they must be created . For objects to be contained in universes-of-discourse, they must be declared . And finally, for objects to be contained in theory-derivations , they must be included (aka postulated).

Footnotes

1

⌜category⌝ is used in its ordinary sense, i.e. not its mathematical sense.