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# independent probability (independentProbability)

One of the basic ProbabilityRelations. (independentProbability formula1 formula2) means that the probabilities of formula1 and formula2 being true are independent.

## Ontology

SUMO / BASE-ONTOLOGY

## Class(es)

 class

inheritable relation

probability relation
 class

inheritable relation

binary predicate
 symmetric relation

independent probability

## Coordinate term(s)

probability fn  arc weight  authors  before or equal  causes  causes subclass  citizen  closed on  conditional probability  connected  connected engineering components  contains information  cooccur  copy  date  decreases likelihood  developmental form  disjoint  distributes  documentation  duration  earlier  editor  element  employs  equal  equivalence relation on  exploits  expressed in language  faces  family relation  finishes  frequency  graph part  greater than  greater than or equal to  has purpose  has skill  holds during  holds obligation  holds right  hole  identity element  in list  in scope of interest  increases likelihood  inhabits  inhibits  initial list  instance  inverse  irreflexive on  larger  less than  less than or equal to  material  measure  meets spatially  meets temporally  modal attribute  overlaps partially  overlaps spatially  overlaps temporally  parent  partial ordering on  partly located  path length  possesses  precondition  prevents  property  publishes  range  range subclass  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  temporal part  time  total ordering on  trichotomizing on  uses  valence  version

## Type restrictions

independentProbability(formula, formula)

## Axioms (3)

increases likelihood and decreases likelihood are disjoint.
`(disjointRelation increasesLikelihood decreasesLikelihood independentProbability)`

If probability of formula1 and formula2 is independent and "the probability of formula2" is equal to number1 and probability of formula1 provided that formula2 holds is formula2, then number2 is equal to number1.
```(=>
(and
(independentProbability ?FORMULA1 ?FORMULA2)
(equal
(ProbabilityFn ?FORMULA2)
?NUMBER1)
(conditionalProbability ?FORMULA1 ?FORMULA2 ?NUMBER2))
(equal ?NUMBER2 ?NUMBER1))```

If formula1 is an instance of formula and formula2 is an instance of formula, then formula1 increases likelihood of formula2 or formula1 decreases likelihood of formula2 or probability of formula1 and formula2 is independent.
```(=>
(and
(instance ?FORMULA1 Formula)
(instance ?FORMULA2 Formula))
(or
(increasesLikelihood ?FORMULA1 ?FORMULA2)
(decreasesLikelihood ?FORMULA1 ?FORMULA2)
(independentProbability ?FORMULA1 ?FORMULA2)))```