# Algernon fundamental taxonomy

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.

## Taxonomy

• 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

## Rules

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

isa(x, s2)
if (@@if-added)

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

r (x, z)
if

## Slot declarations

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 member

The 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.

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