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The DM2 is founded upon the International Defence Enterprise Architecture Specification (IDEAS) (http://www.ideasgroup.org or http://en.wikipedia.org/wiki/IDEAS_Group) a formal ontology foundation developed by the defense departments and ministries of the United States, United Kingdom, Canada, Australia, and Sweden in coordination the North Atlantic Treaty Organization (NATO). All DoDAF concepts and concept relationships inherit several rigorously defined mathematical properties from the IDEAS Foundation. A view of the upper levels of the IDEAS Foundation is shown in the figure below.
IDEAS Foundation Top-Level
The IDEAS Foundation is higher-order. It is extensional (see Extension [metaphysics]), using physical existence as its criterion for identity. In practical terms, this means the ontology is well suited to managing change-over time and identifying elements with a degree of precision that is not possible using names alone. The methodology for defining the ontology is very precise about criteria for identity by grounding reasoning about whether two things are the same using something that can be accurately identified. So, comparing two individuals, if they occupy precisely the same space at the same time, they are the same. Clearly this only works for individuals, but the principle can be used to compare types too. For two types to be the same, they must have the same members. If those members are individuals, their physical extents can be compared. If the members are types, then the analysis continues until individuals are reached, then they can be compared. The advantage of this methodology is that names are separated from things and so there is no possibility of confusion about what is being discussed. It is also four dimensionalist so that temporal parts (or states) can be represented, along with before-after behaviors. A partial bibliography of research and reference material used in deriving the IDEAS Foundation is included in the appendix to this document.
None of these foundation properties are unusual; they are all used in reasoning everyday. The basic concepts are:
Types include sets of Tuples and sets of sets.
Tuples can have other Tuples in their tuple places.
The participants in a super-subtype relationship can be from the same class, e.g., the supertype can be an instance of Measure Type as well as the subtype. This allows for representation of as much of a super-subtype taxonomy as is needed.
The DM2 utilizes the formal ontology of IDEAS because it provides:
The advantage over free-text, structured documents, and databases in using this type of mathematically structured information is somewhat explained by the figure below that shows a spectrum of information structuring.
A Spectrum of Information Structuring
This shows that databases are really just storage and retrieval with connections only for exactly matching pieces of information (e.g., "keys" or exactly matching strings). The nature and purposes of EA require more than just storage, retrieval, and exchange, e.g., integration, analysis, and assessment across datasets. Founding DM2 on IDEAS provides the ontologic foundation supports entailment and other sorts of mathematical understanding of the data with membership (~ set theory) and 4D mereotopology (parts and boundaries). Some of these structures are so fundamental in human reasoning that it's hard to see that computers don't have it at all. But they are needed if we want to use them for something more than just storage and retrieval. They have to be encoded it into them with formal methods.
The re-use patterns useful to Architectural Descriptions are shown in the figure below.
DM2 Common Patterns
The IDEAS foundation concepts, common to all data groups are shown in the table below. It is important to remember that even though these are not repeated in the descriptions of the data groups, they are nevertheless present in the model and apply to the data group concepts according to the Doman Class Hierarchy shown in the figures below.
IDEAS Foundation Concepts Applicable to all DoDAF Data Groups
A RepresentationScheme and DescriptionType whose members are intentionally descriptions
A specific thing that can perform an action
Information is the state of a something of interest that is materialized -- in any medium or form -- and communicated or received.
Category or type of information
A point or extent in space that may be referred to physically or logically.
The powertype of Location
The magnitude of some attribute of an individual.
A category of Measures
Any entity - human, automated, or any aggregation of human and/or automated - that performs an activity and provides a capability.
A SignType where all the individual Signs are intended to signify the same Thing.
A RepresentationType that is a collection of Representations that are intended to be the preferred Representations in certain contexts.
Data, Information, Performers, Materiel, or Personnel Types that are produced or consumed.
A principle or condition that governs behavior; a prescribed guide for conduct or action
A measurement of the performance of a system or service.
The union of Individual, Type, and tuple.
A couple that represents that the temporal extent end time for the individual in place 1 is less than temporal extent start time for the individual in place 2.
An association between two Individual Types signifying that the temporal end of all the Individuals of one Individual Type is before the temporal start of all the Individuals of the other Individual Type.
A tuple that asserts that Information describes a Thing.
A representationSchemeInstance that asserts a Description is a member of a DescriptionScheme.
A temporal whole part couple that relates the temporal boundary to the whole.
A temporal whole part couple that relates the temporal boundary to the whole taken over a Type.
endBoundary is a member of Measure
startBoundary is a member of Measure
endBoundaryType is a member of Measure
startBoundaryType is a member of Measure
A couple that asserts that a Name describes a Thing.
A representationSchemeInstance that asserts a Name is a member of a NamingScheme.
A couple of wholePart couples where the part in each couple is the same.
An overlap in which the places are taken by Types only.
A typeInstance that asserts a Representation is a member of a RepresentationScheme.
A couple that asserts that a Representation represents a Thing.
The beginning of a temporalBoundary.
The beginning of a temporalBoundaryType.
An association in which one Type (the subtype) is a subset of the other Type (supertype).
The start and end times for the spatio-temporal extent of an Individual
The start and end times for the Individual members of a Type.
A wholePart that asserts the spatial extent of the (whole) individual is co-extensive with the spatial extent of the (part) individual for a particular period of time.
A couple between two Individual Types where for each member of the whole set, there is a corresponding member of the part set for which a wholePart relationship exists, and conversely
A Thing can be an instance of a Type - i.e. set membership. Note that IDEAS is a higher-order model, hence Types may be instances of Types.
A couple that asserts one (part) Individual is part of another (whole) Individual.
A coupleType that asserts one Type (the part) has members that have a whole-part relation with a member of the other Type (whole).
DM2 Domain Concepts are Subtypes (Extensions) of IDEAS Foundation Concepts
DM2 Associations are Subtyped to IDEAS Mathematical Associations
IDEAS Foundation Mathematics
When creating or analyzing DM2 data, the following mathematical properties should be followed. (Note, this material is incomplete and will be provided in later versions of either DM2 or IDEAS documentation. Additional sources for ontologic mathematics include: 1) National Center for Ontologic Research (NCOR), http://ontology.buffalo.edu/smith/; 2) Direct Model-Theoretic Semantics for OWL 2, http://www.w3.org/TR/2009/REC-owl2-direct-semantics-20091027/)
Type Theory Math