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# path weight fn (PathWeightFn)

A UnaryFunction that maps a GraphPath to the sum of the arcWeights on the GraphArcs in the GraphPath.

## Ontology

SUMO / GRAPH-THEORY

## Class(es)

 Classe

inheritable relation

FunzioneUnaria

path weight fn

## Coordinate term(s)

absolute value fn  abstraction fn  arc cosine fn  arc sine fn  arc tangent fn  back fn  begin fn  begin node fn  cardinality fn  ceiling fn  complement fn  cosine fn  cut set fn  denominator fn  end fn  end node fn  extension fn  floor fn  front fn  future fn  generalized intersection fn  generalized union fn  giga fn  imaginary part fn  immediate future fn  immediate past fn  initial node fn  integer square root fn  kilo fn  list length fn  magnitude fn  mega fn  micro fn  milli fn  minimal cut set fn  nano fn  numerator fn  organization fn  past fn  pico fn  power set fn  predecessor fn  principal host fn  probability fn  property fn  rational number fn  real number fn  reciprocal fn  round fn  signum fn  sine fn  skin fn  square root fn  successor fn  tangent fn  tera fn  terminal node fn  wealth fn  when fn  year fn

## Type restrictions

NumeroReale PathWeightFn(CamminoDelGrafo)

## Axioms (4)

```(=>
(and
(equal
(PathWeightFn ?PATH)
?SUM)
(subGraph ?SUBPATH ?PATH)
(graphPart ?ARC1 ?PATH)
(arcWeight ?ARC1 ?NUMBER1)
(forall
(?ARC2)
(=>
(graphPart ?ARC2 ?PATH)
(or
(graphPart ?ARC2 ?SUBPATH)
(equal ?ARC2 ?ARC1)))))
(equal
?SUM
(PathWeightFn ?SUBPATH)
?NUMBER1)))```

• se ,
• allora "il valore di path" is uguale a "(number1+number2"
• .
```(=>
(and
(equal
(PathWeightFn ?PATH)
?SUM)
(graphPart ?ARC1 ?PATH)
(graphPart ?ARC2 ?PATH)
(arcWeight ?ARC1 ?NUMBER1)
(arcWeight ?ARC2 ?NUMBER2)
(forall
(?ARC3)
(=>
(graphPart ?ARC3 ?PATH)
(or
(equal ?ARC3 ?ARC1)
(equal ?ARC3 ?ARC2)))))
(equal
(PathWeightFn ?PATH)

• se "il cammino col minor costo tra node1 e node2" is uguale a path e "il valore di path" is uguale a number,
• allora per ogni path2 vale: se path2 é un' istanza di "l' insieme di cammini tra node1 e node2" e "il valore di path2" is uguale a number2, allora number2 é più grande di o uguale a number1
• .
```(=>
(and
(equal
(MinimalWeightedPathFn ?NODE1 ?NODE2)
?PATH)
(equal
(PathWeightFn ?PATH)
?NUMBER))
(forall
(?PATH2)
(=>
(and
(instance
?PATH2
(GraphPathFn ?NODE1 ?NODE2))
(equal
(PathWeightFn ?PATH2)
?NUMBER2))
(greaterThanOrEqualTo ?NUMBER2 ?NUMBER1))))```

• se "il il cammino col costo maggiore tra node1 e node2" is uguale a path e "il valore di path" is uguale a number,
• allora per ogni path2 vale: se path2 é un' istanza di "l' insieme di cammini tra node1 e node2" e "il valore di path2" is uguale a number2, allora number2 é minore o uguale a number1
• .
```(=>
(and
(equal
(MaximalWeightedPathFn ?NODE1 ?NODE2)
?PATH)
(equal
(PathWeightFn ?PATH)
?NUMBER))
(forall
(?PATH2)
(=>
(and
(instance
?PATH2
(GraphPathFn ?NODE1 ?NODE2))
(equal
(PathWeightFn ?PATH2)
?NUMBER2))
(lessThanOrEqualTo ?NUMBER2 ?NUMBER1))))```