relation extended to quantities (RelationExtendedToQuantities)

A RelationExtendedToQuantities is a Relation that, when it is true on a sequence of arguments that are RealNumbers, it is also true on a sequence of ConstantQuantites with those magnitudes in some unit of measure. For example, the lessThan relation is extended to quantities. This means that for all pairs of quantities quantity1 and quantity2, (lessThan quantity1 quantity2) if and only if, for some number1, number2, and unit, quantity1 = (MeasureFn number1 unit), quantity2 = (MeasureFn number2 unit), and (lessThan number1 number2), for all units unit on which quantity1 and quantity2 can be measured. Note that, when a RelationExtendedToQuantities is extended from RealNumbers to ConstantQuantities, the ConstantQuantities must be measured along the same physical dimension.

Ontology

SUMO / BASE-ONTOLOGY

Class(es)

class

inheritable relation

relation extended to quantities

Superclass(es)

entity

abstract

relation

relation extended to quantities

Instance(s)

equal less than greater than less than or equal to greater than or equal to multiplication fn addition fn subtraction fn division fn exponentiation fn max fn min fn reciprocal fn remainder fn round fn

Coordinate term(s)

binary function binary predicate binary relation case role function intentional relation list object attitude partial valued relation predicate probability relation propositional attitude quaternary function quaternary predicate quaternary relation quintary predicate quintary relation single valued relation spatial relation temporal relation ternary function ternary predicate ternary relation total valued relation unary function variable arity relation

Related WordNet synsets

See more related synsets on a separate page.

Axioms (2)

if rel is an instance of relation extended to quantities and rel is an instance of ternary relation and number1 is an instance of real number and number2 is an instance of real number and rel(number1,number2,value) holds,
then for all unit holds: if unit is an instance of unit of measure, then rel("number1 unit(s)","number2 unit(s)","value unit(s)") holds

(=>
      (and
            (instance ?REL RelationExtendedToQuantities)
            (instance ?REL TernaryRelation)
            (instance ?NUMBER1 RealNumber)
            (instance ?NUMBER2 RealNumber)
            (holds ?REL ?NUMBER1 ?NUMBER2 ?VALUE))
      (forall
            (?UNIT)
            (=>
                  (instance ?UNIT UnitOfMeasure)
                  (holds
                        ?REL
                        (MeasureFn ?NUMBER1 ?UNIT)
                        (MeasureFn ?NUMBER2 ?UNIT)
                        (MeasureFn ?VALUE ?UNIT)))))

if rel is an instance of relation extended to quantities and rel is an instance of binary relation and number1 is an instance of real number and number2 is an instance of real number and rel(number1,number2) holds,
then for all unit holds: if unit is an instance of unit of measure, then rel("number1 unit(s)","number2 unit(s)") holds

(=>
      (and
            (instance ?REL RelationExtendedToQuantities)
            (instance ?REL BinaryRelation)
            (instance ?NUMBER1 RealNumber)
            (instance ?NUMBER2 RealNumber)
            (holds ?REL ?NUMBER1 ?NUMBER2))
      (forall
            (?UNIT)
            (=>
                  (instance ?UNIT UnitOfMeasure)
                  (holds
                        ?REL
                        (MeasureFn ?NUMBER1 ?UNIT)
                        (MeasureFn ?NUMBER2 ?UNIT)))))