Introduction

The Semantics of Business Vocabulary and Business Rules (SBVR), an OMG standard is used the AIXM business rules in relation with the elements of the AIXM XML data sets. This means that the AIXM XML elements and attributes, together with their definitions and data types, provide the the "business vocabulary" that is used as the basis for the definition of the AIXM business rules.
This section defines an 'SBVR profile', which is tailored to the AIXM needs and which is documented as a number of concepts and conventions applied in the writing of the AIXM business rules. Two previous projects have provided input material for this document:

work done by Pulsar Consulting, under contract for Eurocontrol;
Guidance on Writing AIRM Constraints provided by SESAR Project 08.01.03.

This document is not intended as an exhaustive introduction to SBVR. Apart from reading the full SBVR specification , the following 'SBVR essentials" reading list is suggested:

the first pages in Chapter 10 of the OMG SBVR specification version 1.1;
this presentation available on the Web (in particular slides 5 and 6).

What is new

See Version 2 (starting in 2024)

SBVR Profile for AIXM

SBVR concepts

The following table introduces the concepts used as part of the SBVR Profile for AIXM, including their graphical notation. Note that the use of some graphical notations is simplified as compared to the SBVR standard, such as double underline which is replaced with simple underline. This facilitates the use of standard office tools for the provision of the AIXM set of Business Rules, as double underline is hardly supported.

Concept	SBVR Definition: Unit of knowledge created by a unique combination of characteristics. Representation in profile: Not represented – too general
NounConcept	SBVR Definition: Concept that is the meaning of a noun or noun phrase. Representation in profile (i.e. what AIXM items may appear as NounConcept according to the SBVR profile): Represented by AIXM XML elements and attributes, which may appear as NounConcept. These are mappable to the AIXM UML Classes and properties, as documented in the XML Schema Mapping. Corresponding XML element in the AIXM rules sets (as exported by BRM): <noun_concept> Example: <noun_concept>Airspace</noun_concept>. Graphical style: Bold, underlined and UpperCamelCase or lowerCamelCase (depending on how the noun concept appears in the AIXM XML Schema). If several nouns are concatenated, then they should be separated by a dot (".") symbol. Colour: #008080 Example: AirportHeliport, AirportHeliportTimeSlice, Airspace.timeslice.AirspaceTimeSlice.type, Runway.associatedAirportHeliport, gml:Point
Verb-concept also known as "Fact type"	SBVR Definition: Concept that is the meaning of a verb phrase that involves one or more noun concepts and whose instances are all actualities. Fact is a proposition that is taken as true. <Fact-type> :: = <concept1> <verb> <concept2> Verb Concepts: Business Facts Relations among Concepts Representation in profile (i.e. what AIXM items may appear as Verb-concept according to the SBVR profile): Represented by a relationship between AIXM XML elements (features) Corresponding XML element in the AIXM rules sets (as exported by BRM): <verb_concept> Example: <verb_concept>has</verb_concept>. Graphical style: italic Colour: #0000ff Example: AirportHeliportTimeSlice has name, Runway has-descendant SurfaceCharacetistics, RunwayTimeSlice.associatedAirportHeliport@xlin:href references-to AirportHeliport
Name	SBVR Definition: Name is a concept that corresponds to only one object [thing] used for the designation of an individual concept — a name. Names tend to be proper nouns. Representation in profile (i.e. what AIXM items may appear as Name according to the SBVR profile): Represents Instances, Slots, Enumeration literals, and their assigned Properties CodeList values Numerical values Corresponding XML element in the AIXM rules sets (as exported by BRM): <name> Example: <name>'CTA'</name>, <name>('A', 'B', 'C')</name>, <name>'117.95'</name> Graphical style: surrounded by 'simple quotes' Colour: #339966 Example: 'Sweden', 'CTA', 'CTA_P', 'YES', 'NIL', '117.95' Note: this style is different from the standard SBVR style for Name concepts (double underline) for a practical reasons - the double underline is not well supported on all the platforms and in all the software applications used for the development and maintenance of the AIXM Business Rules. Sometimes, it is necessary to provide a "list of names" (such as 'A', 'B' or 'C') in order to indicate the allowed values for a property (which appears as a NounConcept in SBVR rules). The following style shall be used: opening-bracket, followed by each Name-value surrounded by simple quotes, separated by comma and ending with closing-bracket. Example: ('A','B','C') (note that the quotes and the brackets may also be formatted, just to keep the editing simple)
keyword	SBVR Definition are used to construct statements – the words that can be combined with other designations to form statements and definitions, see sections on Logical Operations, Quantification, Modality and Data Comparison, all these being part of the keyword concept. Representation in profile: No particular mapping to UML model elements Corresponding XML element in the AIXM rules sets (as exported by BRM): <keyword> Example: <keyword>value</keyword>, <keyword>and</keyword>. Graphical Style: Usual text format Colour: #ff9900 Example: It is prohibited that, value, equal-to, and, etc.

NounConcept - special situations

When writing AIXM business rules in SBVR, apart from the simple cases where an XML element name is used, there are also some special cases, as detailed in the following table.

Special case	NounConcept construction rules
Namespace prefix - all elements in the AIXM XSD belong to a namespace. For most, this is the AIXM namespace. Then, there are elements in the GML namespace, xlink namespace, etc.	The namespace needs to be made explicit in the SBVR rules in order to avoid confusions and to make sure that the right property is used in an automatic SBVR-to-code translator. In order to reduce the length of the noun-concepts, the following conventions applies: all noun-concepts that are in the AIXM namespace appear without any prefix (for example: AirportHeliport, AirportHeliportTimeSlice.type, etc.) noun-concepts that are in a different namespace will appear with a prefix that indicates that namespace gml: for elements in the GML namespace (for example AirportHeliport.gml:identifier, etc.) xlink: for elements in the xLink namespace (for example RunwayTimeSlice.relatedAirport.@xlink:href, etc.) event: for the elements in the Event namespace (used for Digital NOTAM) ead-audit: for the elements that are in the EAD Audit extension namespace ead-adr: for the elements that are in the EAD ADR extension namespace
*Concatenation* - when necessary to identify an AIXM XML element that is remote from the current element. For example, a rule defined for the AirportHeliportTimeSlice element that needs to refer to the name attribute of the associated City class.	The "." symbol is used as separator between the concatenated noun concepts. The relative path needs to include all the intermediate element names, as in the following example: AirportHeliportTimeSlice.servedCity.City.name. Note that the separator is also formatted, just to keep the editing simple, although it is not part of respective noun concept.
*XML Attributes* - For example, most "Val…" data types come with a "uom" attribute.	The attribute name is prefixed with the '@', which is a common convention in XPath and other XML-related languages. For example, the rules that require the mandatory presence of a uom value for an elevation use the following noun concept path: elevation@uom.
TimeSlice - Not present in the UML model, but appearing directly in AIXM XML Schema, based on the AIXM Temporality Concept (see in particular section 3.8 - "Temporality applied to the abstract model"). Most rules refer to descendant elements of a particular TimeSlice.	The following properties, introduced for each and every AIXM <<feature >> class, may appear as noun concepts: timeSlice *"Feature"TimeSlice* where "Feature" is one of the AIXM UML classes with <<feature>> stereotype interpretation sequenceNumber correctionNumber gml:validTime featureLifeime Note: in order to avoid confusions, these properties appear in the SBVR formulation as properties of timeSlice.AIXM Feature TimeSlice.
*GML elements* - Present only partially in the UML model, through the GM_… classes. However, the details of these classes are missing in AIXM 5.1. For example, positions are encoded with the gml:pos element, while surfaces use much deeper structures, such as gml:Surface.gml:...	Specific GML 3.2.1 schema elements appear as NounConcepts, such as: ….gml:Curve.gml:segments.gml:GeodesicString
*Different instances* - When a rule concerns two different instances of the same NounConcept and it is necessary to distinguish between the two. For example, a rule for the uniqueness of 5-letter designators needs to refer to different instances of the DesignatedPoint class.	A number in square brackets is used in order to distinguish the two, such as in the following example: DesignatedPoint[1] Note that this notation is different from the one used in the SBVR standard (subscript, such as DesignatedPoint₁) for a practical reason - subscripts are not well supported in all systems and on all the platforms used for the definition and maintenance of the AIXM Business Rules. This situation might change in future and the graphical notation might be aligned with the one used in the SBVR standard.
::dataSet - In addition to the names of the AIXM elements and attributes, a special name can be used for the identification of the whole data set on which the rules are verified.	Used as ::dataSet

Fact-types

The following table introduces all fact-types used in AIXM SBVR Profile.

has	associative fact type that is defined with respect to a first given concept and a second given concept such that each instance of the fact type is an actuality that an instance of the second concept constitutes an essential quality of an instance of the first concept "has*" as fact type for the child elements:* there is an implicit association (fact type) between an element and each of its child elements. For example: "AirspaceTimeSlice has type"
has-descendant	describes a deeper associative fact than "has"; an instance of the first concept constitutes a child of a child (and so on…) of an instance of the second concept
references-to	indicates the action of identifying a target feature using the value of an xlink:href attribute of a current source feature, taking into consideration the associations implementation method used (according to the AIXM Feature Identification and reference document)
is-referenced-by	indicates the action of identifying a source feature that has an xlink:href attribute pointing to the current target feature, taking into consideration the associations implementation method used (according to the AIXM Feature Identification and reference document)

Keywords - Logical Operations

The following table introduces the logical operations (e.g. "not", "and", "or", etc.) used in the SBVR Profile for AIXM. The exact representation of the operations is in the second column (using keywords convention).

Logical Operation	SBVR Profile for ATM Representation	Meaning
conjunction	p and q	True when all operands are true
disjunction	p or q	True when at least one operand is true
logical negation	not p	True when the operand is false

Keywords - Quantification

The following table introduces the quantifications (e.g. "at least one") used as part of the SBVR Profile for AIXM. The second column contains the representation (using keywords convention).

quantifier name	SBVR Profile for ATM Representation	logic symbol	description
at least n	at-least n x	∃n.. (n ≥ 1)	There is at least n of x Note: n is always instantiated by a number ≥ 1. So this is really a set of quantifiers (n = 1, etc.) Note: for readability reasons, "1" may be also written as "one".
more than n	more-than n x	∃n.. (n > 1)	There is at least n+1 of x Note: n is always instantiated by a number ≥ 1. Note: for readability reasons, "1" may be also written as "one".
at most n	at-most n x	∃0..n (n ≥ 1)	There is at most n of x Note: n is always instantiated by a number ≥ 1. So this is really a set of quantifiers (n = 1, etc.)
less than n	less-than n x	∃0..n-1 (n ≥ 1)	There is at most n-1 of x Note: n is always instantiated by a number ≥ 1.
exactly n	exactly n x	∃n (n ≥ 1)	There is at exactly (at least and at most) n of x Note: n is always instantiated by a number ≥ 1. So this is really a set of quantifiers (n = 1, etc.)
numeric range	from n to m x	∃n..m (n ≥ 1) (m ≥ 2)	There is at least n and at most m of x

Keywords - Modality

The following table introduces the modalities (e.g. "It is prohibited that") used in the SBVR Profile for AIXM.

Modality	SBVR Profile for ATM	Meaning
prohibition (negation of permission)	It is prohibited that p	It is obligatory that not p

Keywords - Data Comparison

The following table introduces keywords that are used in this Profile for comparing values of Noun Concepts.

Keyword

Explanation

Way of use in SBVR AIXM Profile

Example

equal-to

existential quantification plus a condition that the referent thing is the same thing (in numerical value) as the referent of the term that comes next

typically used in front of a Name when the item also has to exist . The comparison is done on numerical values, regardless of the format.

distance value equal-to '5'

distance	result
5	True
5.0	True
4	False
NIL (absent)	False

different-from

existential quantification plus a condition that the referent thing is not the same thing (in numerical value) as the referent of the term that comes next

typically used in front of a Name when the item may also be absent. The comparison is done one numerical values, regardless of the format.

distance value different-from '5'

distance	result
5	False
5.0	False
4	True
NIL (absent)	False

Note: a NIL or absent element will generate no value. This cannot be compared with '5', thus the comparison returns False.

existential quantification plus a condition that the referent thing is the same thing (as a string) as the referent of the term that comes next

typically used in front of a Name when the item also has to exist . The comparison is done on string representations (the format matters).

distance value as '5'

distance	result
5	True
5.0	False
4	False
NIL (absent)	False

other-than

existential quantification plus condition that the referent thing is not the same thing (as a string) as the referent of the term that comes next

typically used in front of a Name when the item may also be null. The comparison is done on string representations (the format matters)

distance value other-than '5'

distance	result
5	False
5.0	True
4	True
NIL (absent)	False

as-one-of

existential quantification plus a condition that the referent thing is the same thing as the referent of one of the terms that come next as a list of Names

typically used in front of a list of Names when the item also has to exist.

other-than-one-of

existential quantification plus condition that the referent thing is not the same thing as the referent of the term that comes next

typically used in front of a list of Names, when the item may also be null

higher-than

existential quantification plus a condition that the referent thing is a numerical value that is larger than the referent of the term that comes next

typically used after a noun-concept in the form of a class attribute that takes numerical values, when the item also has to exist

higher-or-equal-to

existential quantification plus a condition that the referent thing is a numerical value that is larger than or equal to the referent of the term that comes next

typically used after a noun-concept in the form of a class attribute that takes numerical values, when the item also has to exist

lower-than

existential quantification plus a condition that the referent thing is a numerical value that is smaller than the referent of the term that comes next

typically used after a noun-concept in the form of a class attribute that takes numerical values, when the item also has to exist

lower-or-equal-to

existential quantification plus a condition that the referent thing is a numerical value that is smaller than or equal to the referent of the term that comes next

typically used after a noun-concept in the form of a class attribute that takes numerical values, when the item also has to exist

starting-with

existential quantification plus a condition that the referent thing is a string value that includes as first substring elements the string term that comes next

contains-substring

existential quantification plus a condition that the referent thing is a string value that includes the string term that comes next

typically used after a noun-concept value, when the item also has to exist

intersects

existential quantification plus a condition that the referent thing is a time interval, a location or an extent that has a common portion or that is fully overlapping with another thing of the same kind.

typically used to compare:

either timeValid properties of two TimeSlices
or Surface properties of two features

when the item also has to exist.

The same term is used in the OGC® WFS Temporality Extension (12-027r4), where it is defined as semantically equivalent to the fes:AnyInteracts operator as defined in OGC® Filter Encoding 2.0 Encoding Standard (09-026r2), 7.9.2

... extent intersects ... extent

... location intersects ... extent

... period intersects ... period

... instance intersects ... period

closer-than d(.d)NM to

existential quantification plus a condition that the geodesic distance between the referent thing to another thing of the same kind is smaller than the value of d(.d)NM

typically used to check the geodesic distance between two properties that have a location

... location closer-than 5.0NM to ... location

further-than d(.d)NM to

existential quantification plus a condition that the geodesic distance between the referent thing to another thing of the same kind is larger than the value of d(.d)NM

typically used to check the geodesic distance between two properties that have a location

... location further-than 5.0NM to ... location

Keywords - Additional

The following table introduces additional keywords that are used in this Profile.

Keyword	Explanation	Way of use in SBVR AIXM Profile
value	existential quantification that the referent element is not null and it has a value that can be extracted and further analysed Important Note: in the current grammar, value is applied only to simple XML elements that have simple content. It is not used for complex XML elements .	for readability reasons (and to comply with the English language syntax), it is usually written as follows: noun-concept value
value unspecified	the referent element is empty (NIL).	for readability reasons (and to comply with the English language syntax), it is usually written as follows: noun-concept value unspecified
location	existential quantification that the referent element is not null and it has values representing a geographical position (including a Coordinate Reference System) that can be extracted and further analysed Important Note: in the current grammar, location is applied only to GML/AIXM objects that have a unique gml:pos child element, e.g. gml:Point, Point, ElevatedPoint.	for readability reasons (and to comply with the English language syntax), it is usually written as follows: noun-concept location
location unspecified	the referent element is empty (NIL). Important Note: in the current grammar, location is applied only to GML/AIXM objects that have a unique gml:pos child element, e.g. gml:Point, Point, ElevatedPoint.	for readability reasons (and to comply with the English language syntax), it is usually written as follows: noun-concept location unspecified
extent	existential quantification that the referent element is not null and it has values representing a geographical extent in the form of a curve or surface (including a Coordinate Reference System) that can be extracted and further analysed Important Note: in the current grammar, location is applied only to GML/AIXM objects that have Curve and Surface descendants, e.g. gml:Curve, Curve, ElevatedCurve, gml:Surface, Surface, ElevatedSurface.	for readability reasons (and to comply with the English language syntax), it is usually written as follows: noun-concept extent
extent unspecified	the referent element is empty (NIL). Important Note: in the current grammar, location is applied only to GML/AIXM objects that have Curve and Surface descendants, e.g. gml:Curve, Curve, ElevatedCurve, gml:Surface, Surface, ElevatedSurface.	for readability reasons (and to comply with the English language syntax), it is usually written as follows: noun-concept extent unspecified
instant	existential quantification that the referent element is not null and it has values representing a time position that can be extracted and further analysed Important Note: in the current grammar, instant is applied only to GML/AIXM objects that have a unique gml:timePosition child element, e.g. gml:TimeInstant	for readability reasons (and to comply with the English language syntax), it is usually written as follows: noun-concept instant
instant unspecified	the referent element is empty (NIL). Important Note: in the current grammar, instant is applied only to GML/AIXM objects that have a unique gml:timePosition child element, e.g. gml:TimeInstant	for readability reasons (and to comply with the English language syntax), it is usually written as follows: noun-concept instant unspecified
period	existential quantification that the referent element is not null and it has values representing a time period that can be extracted and further analysed Important Note: in the current grammar, period is applied only to GML/AIXM objects that are of type gml:TimePeriod. If the beginPosaition and/or the endPosition are "indeterminate", then the time period is considered to start at -infinite and/or end at +infinite	for readability reasons (and to comply with the English language syntax), it is usually written as follows: noun-concept period
period unspecified	the referent element is empty (NIL). Important Note: in the current grammar, period is applied only to GML/AIXM objects that are of type gml:TimePeriod.	for readability reasons (and to comply with the English language syntax), it is usually written as follows: noun-concept period unspecified

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