W3C

Schema mathematical built-in functions

This is an ontology for computable math functions.

The vocabulary is published by the W3C Notation-3 Community Group.

Vocabulary Terms

Class Definitions
math:Function Function (link)

A math:Function is unique in terms of math:EqualTo.

rdfs:subClassOf
owl:FunctionalProperty
math:List List (link)

The class of things that are N3 lists where all of the members are math:Value items.

rdfs:subClassOf
log:List
math:LogicalOperator math:LogicalOperator (link)

A logical operator allows evaluation eihter way, or testing relationship between two values

rdfs:subClassOf
math:Function, math:ReverseFunction
math:ReverseFunction math:ReverseFunction (link)

A math:ReverseFunction is unambiguous in terms of math:EqualTo.

rdfs:subClassOf
owl:InverseFunctionalProperty
math:StrictProperty StrictProperty (link)

The class of things that compare values.

rdfs:subClassOf
rdf:Property
math:TwoMemberedList TwoMemberedList (link)

This is the class of things that are math lists with only two members.

rdfs:subClassOf
math:List
math:Value Value (link)

The class of things that derive from XSD numeric datatypes.

rdfs:subClassOf
_:b0
Property Definitions
math:absoluteValue negation (link)

The object is calulated as the absolute value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value
math:acos acos (link)

The object is calulated as the arc cosine value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value
math:asin asin (link)

The object is calulated as the arc sine value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value
math:atan atan (link)

The object is calulated as the arc tangent value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value
math:cos cos (link)

The subject is an angle expressed in radians. The object is calulated as the cosine value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value
math:cosh cosh (link)

The subject is an angle expressed in radians. The object is calulated as the #hyperbolic cosine value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value
math:degrees degrees (link)

The subject is an angle expressed in radians. The object is calulated as the conversion in degrees of the value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value
math:difference difference (link)

The subject is a pair of numbers. The object is calculated by subtracting the second number of the pair from the first.

rdfs:domain
math:TwoMemberedList
rdfs:range
math:Value
math:equalTo equalTo (link)

schema: $a1 math:equalTo $a2

summary: checks equality of numbers

definition: true if and only if $a1 is equal to $a2.

requires: $a_1 or $a_2 (or both) must be either concrete numerals, or variables bound to a numeral.

literal domains:

  • $a1: xs:decimal (or its derived types), xs:float, or xs:double (see note on type promotion, and casting from string)
  • $a2: xs:decimal (or its derived types), xs:float, or xs:double (see note on type promotion, and casting from string)
rdfs:domain
math:Value
rdfs:range
math:Value
math:exponentiation exponentiation (link)

The subject is a pair of numbers. The object is calculated by raising the first number of the power of the second.

rdfs:domain
math:TwoMemberedList
rdfs:range
math:Value
math:greaterThan greaterThan (link)

True iff the subject is a number which is greater than the object.

rdfs:domain
math:Value
rdfs:range
math:Value
math:integerQuotient integerQuotient (link)

The subject is a pair of numbers. The object is calculated by dividing the first number of the pair by the second, ignoring remainder.

vs:term_status
deprecated
rdfs:domain
math:TwoMemberedList
rdfs:range
math:Value
math:lessThan lessThan (link)

True iff the subject is a number which is LESS than a object.

rdfs:domain
math:Value
rdfs:range
math:Value
math:memberCount memberCount (link)

The number of items in a list. The subject is a list, the object is calculated as the number of members. Obsolete, see list:length

vs:term_status
deprecated
rdfs:domain
math:List
rdfs:range
math:Value
math:negation negation (link)

The subject or object is calculated to be the negation of the other.

rdfs:domain
math:Value
rdfs:range
math:Value
math:notEqualTo notEqualTo (link)

True iff the subject is a number which is NOT EQUAL to a object.

rdfs:domain
math:Value
rdfs:range
math:Value
math:notGreaterThan notGreaterThan (link)

True iff the subject is a number which is NOT greater than the object.

rdfs:domain
math:Value
rdfs:range
math:Value
math:notLessThan notlessThan (link)

True iff the subject is a number which is NOT LESS than a object.

rdfs:domain
math:Value
rdfs:range
math:Value
math:product product (link)

The subject is a list of numbers. The object is calculated as the arithmentic product of those numbers.

rdfs:domain
math:List
rdfs:range
math:Value
math:quotient quotient (link)

The subject is a pair of numbers. The object is calculated by dividing the first number of the pair by the second.

rdfs:domain
math:TwoMemberedList
rdfs:range
math:Value
math:remainder remainder (link)

The subject is a pair of integers. The object is calculated by dividing the first number of the pair by the second and taking the remainder.

rdfs:domain
math:TwoMemberedList
rdfs:range
math:Value
math:rounded rounded (link)

The object is calulated as the number with no fractional part that is closest to the subject. If there are two such numbers, then the one that is closest to positive infinity is returned.

rdfs:domain
math:Value
rdfs:range
math:Value
math:sin sin (link)

The subject is an angle expressed in radians. The object is calulated as the sine value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value
math:sinh sinh (link)

The subject is an angle expressed in radians. The object is calulated as the hyperbolic sine value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value
math:sum sum (link)

schema: ($a_1 .. $a_n) math:sum $a_s

summary: performs addition of numbers

definition: true if and only if the arithmetic sum of $a_1, .. $a_n equals $a_s.

requires: all $a_1, .., $a_n to be bound.

literal domains:

  • $a_1 .. $a_n : xs:decimal (or its derived types), xs:float, or xs:double (see note on type promotion, and casting from string)
  • $a_s: xs:decimal (or its derived types), xs:float, or xs:double (see note on type promotion, and casting from string)
rdfs:domain
log:List
rdfs:range
math:Value
math:tan tan (link)

The subject is an angle expressed in radians. The object is calulated as the tangent value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value
math:tanh tanh (link)

The subject is an angle expressed in radians. The object is calulated as the hyperbolic tangent value of the subject.

rdfs:domain
math:Value
rdfs:range
math:Value