This is a transcription of the taxonomy of fundamental objects in algernon.

This is maintained as
HTML but it's converted to RDF form using a transformation. Use the namespace name `
http://www.w3.org/2000/07/hs78/algernon#` to refer to these properties
and classes in RDF 1.0 syntax.

@@TODO: express the relationship between algernon:subset and rdfs:subClass, etc.

**things****rules****objects****sets**e.g.*things**objects**sets**slots***booleans**e.g.*true**false*@@:complete**contexts**e.g.*global-context*

**slots****order-relations****tc-order-relations****equivalence-relations**

*@@this is an if-added rule on things. We could use some "for all things
x ... " notation. hmm...*.

- isa(
`x`,`s2`) - if (@@if-added)
- isa(
`x`, things) - isa(
`x`,`s1`) - imp-superset(
`s1`,`s2`)

- isa(

here's a "slot rule", i.e. quantification over slots (predicates)

`r`(`x`,`z`)- if
- isa(
`r`, transitive-relations) `r`(`x`,`y )``r`(`y`,`z`)

- isa(

or, in RDF terms, properties

**isa**: things -> sets(isa ?x ?s) = ?x is a member of the set ?s.

**member**:*sets*->*things*

@@:backlink isa(member ?s ?x) = A member of ?s is ?x.

**subset**:*sets*->*sets*(subset ?s1 ?s2) = A subset of ?s1 is ?s2.

**superset**:*sets*->*sets*

@@:inverse subset(superset ?s1 ?s2) = A superset of ?s1 is ?s2.

**selfset**:*things*->*sets*

@@:cardinality 1

@@:backlink memberThe selfset of x is the set {x}.

**less**:*objects*->*objects*(less ?x ?y) = ?x less than ?y.

**greater**:*objects*->*objects*

@@:inverse less(greater ?x ?y) = ?x greater than ?y.

**equal**:*objects*->*objects*

@@:inverse equal(equal ?x ?y) = ?x is equal to ?y.

**least**:*objects*->*sets*(least ?x ?s) = ?x is the least member of ?s.

**greatest**:*objects*->*sets*(greatest ?x ?s) = ?x is the greatest member of ?s.

$Revision: 1.13 $ of $Date: 2000/07/25 05:16:29 $ by $Author: connolly $