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).

Ontologie

SUMO / BASE-ONTOLOGY

Class(es)

třída

inheritable relation

binární predikát
is instance of

nesymetrická relace
is instance of

trichotomizing on

Související termín(y)

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

Typy argumentů

trichotomizingOn(binární relace, množina nebo třída)

Axiomy (6)

less than je trichotomizing on reálné číslo.

(trichotomizingOn lessThan RealNumber)

greater than je trichotomizing on reálné číslo.

(trichotomizingOn greaterThan RealNumber)

less than or equal to je trichotomizing on reálné číslo.

(trichotomizingOn lessThanOrEqualTo RealNumber)

greater than or equal to je trichotomizing on reálné číslo.

(trichotomizingOn greaterThanOrEqualTo RealNumber)

relation je total ordering on class tehdy a jen tehdy pokud relation je partial ordering on class a relation je trichotomizing on class.

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

jestliže relation je trichotomizing on class,
potom pro všechny inst1,inst2 platí: jestliže inst1 je instancí třídy class a inst2 je instancí třídy class, potom relation(inst1,inst2) holds nebo relation(inst2,inst1) holds nebo inst1 se rovná 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)))))