trichotomizing on (trichotomizingOn)

A BinaryRelation rel is trichotomizing on a SetOrClass only if, for all instances inst1 and inst2 of the SetOrClass, at least one of the following holds: (rel inst1 inst2), (rel inst2 inst1) or (equal inst1 inst2).

Ontology

SUMO / BASE-ONTOLOGY

Class(es)

Classe

inheritable relation

PredicatoBinario
is instance of

RelazioneAsimmetrica
is instance of

trichotomizing on

Coordinate term(s)

back fn cardinality fn front fn principal host fn probability fn skin fn arc weight attribute authors before or equal causes causes subclass citizen closed on completely fills connected contains information cooccur copy crosses date decreases likelihood developmental form disjoint distributes documentation duration earlier editor element employs equal equivalence relation on exploits expressed in language faces family relation fills finishes frequency graph part greater than greater than or equal to has purpose has skill holds during holds obligation holds right hole identity element immediate instance immediate subclass in list in scope of interest increases likelihood independent probability inhabits inhibits initial list instance inverse irreflexive on larger less than less than or equal to manner material measure meets temporally member modal attribute overlaps temporally parent partial ordering on partially fills partly located path length penetrates possesses precondition prevents proper part properly fills property publishes range range subclass realization refers reflexive on related internal concept sibling smaller starts sub attribute sub collection sub graph sub list sub process sub proposition subclass subrelation subsumes content class subsumes content instance successor attribute successor attribute closure surface temporal part time total ordering on uses valence version

Type restrictions

trichotomizingOn(RelazioneBinaria, InsiemeOClasse)

Axioms (6)

less than é tricotomizzante su NumeroReale.

(trichotomizingOn lessThan RealNumber)

greater than é tricotomizzante su NumeroReale.

(trichotomizingOn greaterThan RealNumber)

less than or equal to é tricotomizzante su NumeroReale.

(trichotomizingOn lessThanOrEqualTo RealNumber)

greater than or equal to é tricotomizzante su NumeroReale.

(trichotomizingOn greaterThanOrEqualTo RealNumber)

relation é ordinamento totale suclass se e solo se relation é ordinamento parziale su class e relation é tricotomizzante su class.

(<=>
      (totalOrderingOn ?RELATION ?CLASS)
      (and
            (partialOrderingOn ?RELATION ?CLASS)
            (trichotomizingOn ?RELATION ?CLASS)))

se relation é tricotomizzante su class,
allora per ogni inst1,inst2 vale: se inst1 é un' istanza di class e inst2 é un' istanza di class, allora relation(inst1,inst2 vales o relation(inst2,inst1 vales o inst1 is uguale a inst2

(=>
      (trichotomizingOn ?RELATION ?CLASS)
      (forall
            (?INST1 ?INST2)
            (=>
                  (and
                        (instance ?INST1 ?CLASS)
                        (instance ?INST2 ?CLASS))
                  (or
                        (holds ?RELATION ?INST1 ?INST2)
                        (holds ?RELATION ?INST2 ?INST1)
                        (equal ?INST1 ?INST2)))))