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# conditional probability (conditionalProbability)

One of the basic ProbabilityRelations. conditionalProbability is used to state the numeric value of a conditional probability. (conditionalProbability formula1 formula2 number) means that the probability of formula2 being true given that formula1 is true is number.

## Ontology

SUMO / BASE-ONTOLOGY

## Class(es)

 class

inheritable relation

probability relation
 class

inheritable relation

ternary predicate

conditional probability

## Coordinate term(s)

probability fn  altitude  between  capability  confers obligation  confers right  connects  decreases likelihood  depth  distance  domain  domain subclass  has purpose for agent  increases likelihood  independent probability  links  occupies position  orientation  prefers  related external concept  represents for agent  represents in language  temporally between  temporally between or equal

## Type restrictions

conditionalProbability(formula, formula, real number)

## Axioms (3)

If formula1 increases likelihood of formula2 and "the probability of formula2" is equal to number1 and probability of formula1 provided that formula2 holds is formula2, then number2 is greater than number1.
```(=>
(and
(increasesLikelihood ?FORMULA1 ?FORMULA2)
(equal
(ProbabilityFn ?FORMULA2)
?NUMBER1)
(conditionalProbability ?FORMULA1 ?FORMULA2 ?NUMBER2))
(greaterThan ?NUMBER2 ?NUMBER1))```

If formula1 decreases likelihood of formula2 and "the probability of formula2" is equal to number1 and probability of formula1 provided that formula2 holds is formula2, then number2 is less than number1.
```(=>
(and
(decreasesLikelihood ?FORMULA1 ?FORMULA2)
(equal
(ProbabilityFn ?FORMULA2)
?NUMBER1)
(conditionalProbability ?FORMULA1 ?FORMULA2 ?NUMBER2))
(lessThan ?NUMBER2 ?NUMBER1))```

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))```