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= [[UoM_Ontology_Standard]] (Reference) UML Model - draft =

Editor: [[DavidLeal|David Leal]]

''This is the workspace for the drafting of the [[UoM_Ontology_Standard]] (Reference) UML Model''

----

== A strawman UML model based upon initial discussions ==

=== Introduction ===

This in an attempt to summarise part of the discussion so far. Very interesting threads about:

* the relationships between quantities and measurement methods;
* non-scalar quantities;
* dimensionless quantities, especially angle;

have not yet been addressed.

=== Sources ===

The principal sources for the strawman have been:

* the International Vocabulary of Metrology - Basic and General Concepts and Associated Terms (VIM) (http://www.bipm.org/en/publications/guides/vim.html);
* a [http://ontolog.cim3.net/file/work/UoM/uom_ontoloogy_progress/uom_ontology_progress-files/NIST_Quantities_Model--EdBarkmeyer_20080825a.pdf UML model derived from VIM], with an [http://ontolog.cim3.net/file/work/UoM/uom_ontoloogy_progress/uom_ontology_progress-files/Scales--DavidLeal_20090724a.png extension for scales], developed by a team including NIST, which was supplied by Ed Barkmeyer;
* content of the e-mail discussion on [ [http://ontolog.cim3.net/forum/uom-ontology-std/ uom-ontology-std] ].

=== A strawman for quantity ===

A strawman UML diagram for "quantity" is: http://ontolog.cim3.net/file/work/UoM/uom_ontoloogy_progress/uom_ontology_progress-files/strawman_UML_for_quantity--DavidLeal_20090724a.gif

The differences between the Strawman and the original UML diagram supplied by Ed, include the following:

* The concept "quantity" has been split into '''generic quantity''' and '''particular quantity'''.
* The concept '''magnitude of quantity''' has been introduced.
* A '''quantity value''' does not necessarily reference a unit. This is not what the VIM says. There are a number of things which could be referenced, including a unit.
* The concept '''particular phenomenon body or substance''' has been introduced. This seems appropriate because quantities do not exist without something to possess them.

The UML diagram does not purport to be an ontology, but is an informal representation of the concepts related to "quantity" that have been discussed so far and their relationships.

The text associated with the UML objects shows an unsolved problem, as follows:

* Rockwell C hardness (150 kg) is shown as an example of '''generic quantity'''. It seems appropriate to include Rockwell C hardness (150 kg) as a '''generic quantity''' alongside thickness or radius, because it is something that can be measured for a particular solid object.
* Rockwell C hardness (150 kg) is shown as an example of '''kind of quantity'''. It seems appropriate to include Rockwell C hardness (150 kg) as a '''kind of quantity''' alongside length, because a measurement of Rockwell C hardness (150 kg) provides an expression of a ''magnitude of quantity'' that is within Rockwell C hardness (150 kg). Similarly a measurement of radius provides an expression of a '''magnitude of quantity''' that is within length.

The same would be true of mass.

=== Distinction between magnitude of quantity and quantity value ===

In the strawman UML diagram, '''quantity value''' is a data structure that expresses a '''magnitude of quantity'''. This is a valid interpretation of the VIM. With this interpretation, 5.34 m and 534 cm are two different instances of '''quantity value''' which express the same '''magnitude of quantity'''.

However, the clause that defines '''quantity value''' contains "NOTE 3 A '''quantity value''' can be presented in more than
one way." This note implies a different terminology, but not a different model structure. Taking account of this note:

* '''magnitude of quantity''' in the strawman UML would be called '''quantity value''';
* '''quantity value''' in the strawman UML would be called '''quantity presentation'''.

=== Discussion of Rockwell C hardness ===

It seems straightforward that Rockwell_C_hardness_(150kg) is a '''kind of quantity'''. Within this '''kind of quantity''', the there is a '''magnitude of quantity''' that is expressed by the '''quantity value''' (55, Rockwell_C_hardness_(150_kg)). So far so good - this is consistent with the strawman UML model. Note that in this case the reference from the '''quantity value''' is not a unit but a measurement procedure.

The difficulty is the relationship between my_lump_of_hard_steel and the '''magnitude of quantity''' that is expressed as (55, Rockwell_C_hardness_(150_kg)). One approach is to regard the '''magnitude of quantity''' as the class of objects that have the specified response the the measurement procedure. Hence in this case, the link between '''magnitude of quantity''' and '''particular phenomenon body or substance''', which is labelled ''particular quantity''', is classification.

The relationship is not always classification, because consider waterline length of a ship. If the ship Medway_Queen has a waterline length of 20 metres, then we have:

* the '''particular phenomenon body or substance''' that is the Medway_Queen;
* the '''magnitude of quantity''' thas is expressed by the '''quantity value''' (20, metre);
* the '''particular quantity''' relationship has_waterline_length between the two.
In this case, the '''particular quantity''' relationship is of a special type - has_waterline_length.

The relationship has_waterline_length is a shorthand for something quite complicated. There is a relationship has_extreme_waterline_point_pair between a ship and a point pair. Just as the '''magnitude of quantity''' that is expressed as (55, Rockwell_C_hardness_(150_kg)) can be regarded as a class with solid objects as members, the '''magnitude of quantity''' that is expressed as (20, metre) can be regarded as a class that has point pairs as members.

Hence for the ship there are two relationships: has_extreme_waterline_point_pair and classification, which are composed to give has_waterline_length. This seems to be a very common case, where the nature of the relationship between a physical object and a '''magnitude of quantity''' embodies a great deal of domain knowledge, and the '''kind of quantity''' is simple. For Rockwell hardness the relationship is simply classification, and the domain knowledge is embodied in the '''kind of quantity'''. The strawman UML model handles both.

VIM defines '''kind of quantity''' as "aspect common to mutually comparable quantities". Hence Brinnel Hardness (653, HBW) and the Rockwell C hardness (60, HRC) are not of the same '''kind of quantity''' because they cannot be compared in general, although comparison may be possible for a particular class of material. There is a engineering understanding of the general concept that the Brinnel and Rockwell procedures are intended to measure - i.e. "hardness". This is not a '''kind of quantity''' as defined in the VIM, but is a useful concept nonetheless.

=== A strawman for system of quantities ===

A strawman UML diagram for '''system of quantities'' is: http://ontolog.cim3.net/file/work/UoM/uom_ontoloogy_progress/uom_ontology_progress-files/strawman_UML_for_system_of_quantities--DavidLeal_20090724a.gif

It was pointed out during the discussion that:

* there can be many different systems of quantities, with different base and derived quantities;
* a system of quantities is not the same as a system of units.

Both conclusions are also contained within the VIM. Hence being a '''base quantity''' or '''derived quantity''' is not a inherent property of a '''kind of quantity''', but a relationship between a '''kind of quantity''' and a '''system of quantities'''.

=== A strawman for system of units ===

The text in the VIM says that a '''base unit''' or '''derived unit''' for a '''system of units''' correspond to a '''base quantity''' or '''derived quantity''' respectively. The VIM does not say that there is anything special in the way in which a unit is defined that makes it a base unit or derived unit.

A strawman UML diagram for '''system of units''' that is analogous to the diagram for '''system of quantities''' is: http://ontolog.cim3.net/file/work/UoM/uom_ontoloogy_progress/uom_ontology_progress-files/strawman_UML_for_system_of_units--DavidLeal_20090724a.gif

The original UML diagram supplied by Ed contains the text definition "A base unit is defined by a physical phenomenon, i.e., a 'definite description'". Following this approach it is natural to make '''base unit''' a subclass of '''measurement unit'''. However an "off-system measurement unit" may also be defined by a physical phenomenon. Hence it may be best to add this as: http://ontolog.cim3.net/file/work/UoM/uom_ontoloogy_progress/uom_ontology_progress-files/strawman_UML_for_unit_defined_by_a_physical_phenomenon--DavidLeal_20090724a.gif

=== A strawman for scale ===

The discussion so far has recognised the importance of scales, but has not gone into details. Extracting from the original UML diagram for scales supplied by Ed, and using VIM terminology wherever possible, a strawman UML diagram is: http://ontolog.cim3.net/file/work/UoM/uom_ontoloogy_progress/uom_ontology_progress-files/strawman_UML_for_scale--DavidLeal_20090724a.gif

The object '''space of values''' has been added. For most scales, this is a real or integer interval, perhaps unbounded. However, it could be something else, such as a sequence of letters "a", "b", "c", etc..

VIM does not give an example of '''conventional reference scale'''. Perhaps ITS90 (http://www.bipm.org/en/publications/its-90.html) is such a scale.

The relationship between scales and units has not been addressed in this strawman.

== Relationship between the strawman UML model and [[UnitsML]] ==

[[UnitsML]] has much important content relevant to symbols, prefixes and units conversion. However the only those parts of [[UnitsML]] relevant to the strawman diagrams for '''quantity''', '''system of quantities''', '''unit''', '''system of units''' and '''scale''' are considered here. Some relationships between objects and relationships in the strawman and elements and attributes in [[UnitsML]] are as follows:

:'''kind of quantity''': The object in the strawman corresponds to the element ''Quantity'' in [[UnitsML]].

:'''measurement unit''': The object in the strawman broadly corresponds to the element ''Unit'' in [[UnitsML]]. However, Fahrenheit is regarded as an instance of ''Unit'', whereas in the strawman it would be an instance of '''scale'''.

:'''quantity value''': The object in the strawman does not corresponds to an element in [[UnitsML]]. Instead the presence of a [[UnitsML]] ''Unit'' element as a child of an element defined elsewhere represents a '''reference for quantity value''' relationship.

:'''magnitude of quantity''': The object in the strawman is outside the scope of [[UnitsML]], except when it is a '''measurement unit'''.

:'''magnitude is within''': This relationship between '''magnitude of quantity''' and '''kind of quantity''' is outside the scope of [[UnitsML]] except when the '''kind of quantity''' is a '''measurement unit'''. In this case, the relationship is provided within [[UnitsML]] by the child element ''QuantityReference'' of ''Unit''.

:'''quantity dimension''': The object in the strawman corresponds to the element ''Dimension'' in [[UnitsML]].

:'''has dimension''': This relationship between '''kind of quantity''' and '''dimension''' is provided within [[UnitsML]] by the attribute ''dimensionURL'' of ''Quantity''. [[UnitsML]] allows a dimension to be specified for a ''Unit''. In the strawman, this is superfluous because a a '''measurement unit''' is of exactly one '''kind of quantity''' for which a '''dimension''' can be specified.

== Relationship between the strawman UML model and [http://aurora.regenstrief.org/~ucum/ucum.html The Unified Code for Units of Measure (UCUM)] ==

The UCUM has much important content concerning a formal algebra for the derivation of units. The elements ''unit'' and ''base-unit'' within the UCUM XML schema corresponds to the object '''measurement unit''' in the strawman.

== Relationship between the strawman UML model and the [http://mymobileweb.morfeo-project.org/ [[MyMobileWeb]]] [http://idi.fundacionctic.org/muo/ Measurement Units Ontology (MUO)] ==

The [[MyMobileWeb]] has assimulated the UCUM units as instances of a class within a larger ontology. Some relationships between objects and relationships in the strawman and elements and attributes in MUO are as follows:

:'''kind of quantity''': The object in the strawman corresponds to the class ''PhysicalQuality'' in the MUO. The MUO is admirably precise in specifying that it is not a '''particular quantity'''.

:'''measurement unit''': The object in the strawman broadly corresponds to the class ''[[UnitOfMeasurement]]'' in the MUO. However, Fahrenheit is regarded as an instance of ''[[UnitOfMeasurement]]'', whereas in the strawman it would be an instance of '''scale'''.

:'''quantity value''': It is natural to associate this object in the strawman with the class ''QualityValue'' in the MUO. This is probably broadly true, but in the MUO ''QualityValue'' has the property ''inTime'' which specifies when the value occurs. In the strawman, time is more appropriately associated with the '''particular quantity''' or with the temporal part of the '''particular phenomenon body or substance''' that possesses it.

== Relationship between the strawman UML model and the proposed [[UoM]] extension to [[SysML]] ==

Clause "C.5 Model Library for Quantities, Units, Dimensions and Values (QUDV)" is a proposed addition to the [[SysML]] specification [http://www.omg.org/spec/SysML/1.1 ]. It is currently being considered by the [[SysML]] Revision Task Force (RTF). If accepted, it will become a non-normative annex of the [[SysML]] 1.2 specification.

Figure C.8 QUDV Concepts diagram has much the same scope as the strawman UML diagrams. Both are derived from the VIM, and are therefore similar. Some differences are:

* The proposed [[SysML]] diagram has a many to many relationship between [[SystemOfUnits]] and [[SystemOfQuantities]]. The VIM says that a '''system of units''' is "defined ... for a given system of quantities". Hence in accordance with the VIM, the strawman UML says that a '''system of units''' has a relationship with exactly one '''system of quantities'''.

* The proposed [[SysML]] diagram has not sought to separate the different concepts within the concept called "quantity" by the VIM.

* The proposed [[SysML]] diagram renames "kind of quantity" in the VIM as "QuantityKind". (There is belief in the USA and Germany that nouns can be placed side by side with an implicit relationship. There is a belief in the UK and France that the relationship should be stated explicitly by a preposition. :)

In Figure C.10 QUDV QuantityKind diagram, the class "QuantityKind" has a subclass "[[DerivedQuantityKind]]". This is incorrect, because a '''kind of quantity''' may be a base quantity in one '''systems of quantities''', but a derived quantity in another. The '''kind of quantity''' ''electric charge'' is an example of this.

== Formal definitions of key concepts related to quantity ==

'''Q1 particular quantity''': class of individual quantifiable properties of individual things (the tropes)

Examples: The length of my thumb (and no one else's thumb).

'''Q2 kind of quantity (as class of particular quantity)''': class whose members are subclasses of '''particular quantity''' in which all the members are comparable

Example: length (as a class of particular quantity). The length of my thumb is a member of length (as a class of particular quantity).

'''Q3 magnitude of quantity''': class whose members are subclasses of '''particular quantity''' in which all the members are equal

Note: A member of '''magnitude of quantity''' is an equivalence class.

Example: The length magnitude called "5cm", which includes the length of my thumb, the height of my coffee cup, and so on.

'''Q4 kind of quantity (as class of magnitude)''': class whose members are subclasses of '''magnitude of quantity''' in which all the members are subclasses of the same '''kind of quantity (as class of particular quantity)'''

Example: length (as a class of '''magnitude of quantity'''). The length magnitude called "5cm" is a member of length (as a class of magnitude of quantity).

Note: '''measurement unit''' is a subclass of 'magnitude of quantity'''. Hence each measurement unit is a member of a '''kind of quantity (as class of magnitude'''. The metre is a member of length (as a class of magnitude).

=== Discussion ===

The definitions of Q1 to Q4 were proposed by Ed Barkmeyer.

The distinction between '''Q2 kind of quantity (as class of particular quantity)''' and '''Q4 kind of quantity (as class of magnitude)''' is not made in the strawman UML diagrams. In the UML diagrams there is a relationship '''magnitude is within''' beween '''magnitude of quantity''' and '''kind of quantity'''. The formal meaning of this relationship depends upon the formal definitions, as follows:

* the relationship between '''magnitude_of_quantity''' and '''kind of quantity (as class of particular quantity)''' is subclass;
* the relationship between '''magnitude_of_quantity''' and '''kind of quantity (as class of magnitude)''' is member.

=== An informal explanation of the different "quantity" concepts ===

The class '''particular quantity''' has properties of things as members, as shown in http://www.caesarsystems.co.uk/uom_ontology_progress/uom_ontology_progress-files/particular_quantity.gif

The members of '''particular quantity''' can be collected into subclasses which are comparable, as shown in http://www.caesarsystems.co.uk/uom_ontology_progress/uom_ontology_progress-files/particular_quantity-kind.gif

Each of these subclasses of '''particular quantity''' is a '''kind of quantity (as class of particular quantity''', as shown in http://www.caesarsystems.co.uk/uom_ontology_progress/uom_ontology_progress-files/kind_of_quantity-class_of_particular_quantity.gif

The members of '''particular quantity''' can be collected into subclasses which are equal, as shown in http://www.caesarsystems.co.uk/uom_ontology_progress/uom_ontology_progress-files/particular_quantity-magnitude.gif

Each of these subclasses of '''particular quantity''' is a '''magnitude of quantity''', as shown in http://www.caesarsystems.co.uk/uom_ontology_progress/uom_ontology_progress-files/magnitude_of_quantity.gif

The members of '''magnitude of quantity''' can be collected into subclasses such that the members of each member are comparable. Each of these subclasses is a '''kind of quantity (as class of magnitude)''' as shown in http://www.caesarsystems.co.uk/uom_ontology_progress/uom_ontology_progress-files/kind_of_quantity-class_of_magnitude_of_quantity.gif

=== Meta-levels of the quantity concepts ===

The meta-levels of the quantity concepts are illustrated by development of the example provided by Hajo Rijgersberg shown in

http://www.caesarsystems.co.uk/uom_ontology_progress/uom_ontology_progress-files/quantity_meta-levels.gif

The only concrete object is "length of my table at my instant", which is a member of '''particular quantity'''. All the others objects are abstractions at different meta-levels. The higher level abstractions may seem unnecessarily complicated, but a justification is as follows:

* "1.3 metres" and "the metre" are both members of '''magnitude of quantity''' and of "length as a class of magnitude" (neither are members of "length as a class of particular quantity" because both are abstractions and not members of '''particular quantity''');
* that "1.3 metres" can be expressed in terms of its relationship with a unit, such as "the metre", is a property of the class "length as a class of magnitude";
* a subclass of '''Q4, kind of quantity as class of magnitude''' can be defined that contains all members for which a simple relationship with a unit exists.

[[Category:WorkSpace]] [[Category:OntologBasedStandards]] [[Category:UoM_Ontology_Standard]]

UoM Ontology Standard UML Model Draft - Revision history

imported>KennethBaclawski: Fix PurpleMediaWiki references