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A property is essential to an individual iff it necessarily holds for that individual
A property is rigid (+R) iff, necessarily, it is essential to all its instances. A property is non-rigid (-R) iff it is not essential to some of its instances, and anti-rigid (~R) iff it is not essential to all its instances
A property carries an identity criterion (+I) iff all its instances can be (re)identified by means of a suitable sameness relation. A property supplies an identity criterion iff such criterion is not inherited by any subsuming property
An individual is concrete iff it has a physical location. A property whose instances are necessarily concrete will be marked with the meta-property +C
Note that an individual can be concrete without being necessarily real , or actual : Peter Pan is not real but is concrete
This meta-property is a bit less formal (in the ontological sense) than the previous ones, since it makes an ontological commitment towards the existence of physical (spatial, temporal or spatio-temporal) locations. We see physical locations as primitive qualities that individuals can have
An individual is unified by a (suitably constrained) relation R iff it is a mereological sum of entities that are bound together by R. Ex. the relation having the same boss may unify a group of employees in a company
An individual w is a whole under R iff it is maximally unified by R , in the sense that R is internal to w , and no part of w is linked by R to something that is not part or w
A property P is said to carry unity (+U) if there is a common unifying relation R such that all the instances of P are essential wholes under R . A property carries anti-unity (~U) if all its instances can possibly be non-wholes. If every instance of P is an essential whole, but there is no unifying relation common to all instances of P , then we mark P with the property *U
An individual is a singular whole iff its unifying relation is the transitive closure of the relation "strong connection", like that existing between two 3D regions that have a surface in common. Topological wholes of this kind have a special cognitive relevance, which accounts for the natural language distinction between singular and plural
A plural individual is a sum of singular wholes that is not itself a singular whole. Plural individuals may be wholes themselves or not. In the former case they will be called collections ; in the latter case pluralities
A piece of coal is a singular whole. A lump of coal is a topological whole, but not a singular whole, since the pieces of coal merely touch each other, with no material connection. It is therefore a plural whole
What distinguishes an object from an aggregate is that the former is an essential whole , namely it has a unity criterion , while the latter is not. For example, John can “make-up” a snowman ( object ) starting from the scattered snow ( amount of matter ) covering his courtyard, adding a hat, a carrot, two deadwoods, etc. In general, amounts of matter are mass-nouns (you can’t say a snow, a water, ...), while objects are count-nouns (such as a snowman, five glasses of water,and so on).
Arbitrary collections are just mere sum of wholes which are not themselves essential wholes (as the collection of goods in a bazar ). In this sense, they are kinds of aggregate . On the other hand, there are collections which are themselves essential wholes, as a library . In our top-level these unitary collections are to be conceived as a specialization of the object category.
An object can change some parts, keeping or not its identity. In the first case, we call it Ordinary Object (~E), in the second case Extensional Object (+E). My car will continue to be the same even if I replace one of its wheels. On the contrary, if I consider the universe , removing a single elementary particle I won’t have the universe any more, but a different entity.
Regarding aggregates , we can say that amounts of matter are clearly +E, while arbitrary collections can be considered as pseudo-extensional (changes in the parts of a member of a collection may be allowed).
Features are “parasitic” (+D) entities, that exist insofar their host exists. Features may be relevant parts of their host, like a bump in a road, or dependent regions , such as a hole in a piece of cheese, the underneath of a table, or the shadow of a tree (which are not parts of their hosts). All features are essential wholes, but no common unity criterion may exist for all of them (*U). Some features can change parts keeping their identity, while some others not: for this reason, we use -E as the common formal property (+E and ~E are both subsumed by -E).
Abstractions are entities that are not concrete, that is, they do not have a physical location (~C). Quality spaces are the first examples of abstractions: time, geometric space, length, color, are all conceptual spaces, with different topological structure. Terms like red, long, sweet, old, recent etc. correspond to regions in a quality space. We can therefore describe the structure of a quality space with a first-order theory, using topological notions: for instance, we can say that “red is adjacent to brown”. Other examples of Abstraction are propositions , sets , symbols , etc.
Qualities are always “qualities of something”: in this sense, they are dependent (+D). Qualities are individual, i.e. that they are inherent to a unique entity ( the color of this rose is red ). We call quality-type every homogenous group of individual qualities, such as color , shape , volume , etc. In the OntoClean top-level qualities are structured in strict relationship with quality spaces : every quality-type “corresponds” to a quality space in the branch of Abstractions . A region in a quality space corresponds to an individual quality of an entity in our conceptualization of the world.
Following our approach, the red of the rose on the right figure is represented as located in a certain region in the colors-quality-space. In the same way, the spherical shape of the ball below is represented as located in a certain region of the shape-quality-space. In principle, time and space could be treated as qualities too. We are currently studying the ontological commitments and the formal properties concerning this options.
Appendix: An Alternative View of the OntoClean Top-Level (1)
Since the agreement on the meaning of general categories is not always easy, in this short presentation we preferred to make clear first the most relevant top-level concepts, leaving aside the various ways they can be presented in a hierarchy. For example, we could have introduced the OntoClean top-level by considering the general distinction between concrete and abstract entities as the complete partition of “what there is” in the world. Then, within concrete entities we could have distinguished independent from dependent entities. The overall taxonomy would have been like this:
Appendix: An Alternative View of the OntoClean Top-Level (2)
Catalog of normalized terms , e.g. a list of terms used in the reports from a laboratory: no taxonomy, no axioms, and no glosses
Glossed catalog , e.g. a dictionary: a catalog with glosses.
Thesaurus , e.g. many parts of the UMLS Metathesaurus, GEMET: a hierarchical collection of terms; the hierarchical link is usually polysemous
Taxonomy , e.g. the ICD10: a collection of classes with a partial order induced by inclusion ( classification )
Axiomatized taxonomy , e.g. the GALEN Core Model: a taxonomy with axioms
Ontology library , e.g. the Ontolingua repository: a set of axiomatized taxonomies with relations among them. Each element of the library is a module , which can be included into another one. Also, a concept from a module can be only used into another one. Ontology modules can be considered subdivisions of the namespace of a model
Ontology integration is – generally speaking – the construction of an ontology C that formally specifies the union of the vocabularies of two other ontologies A and B
To be sure that A and B can be integrated at some level, C has to commit to both A's and B's conceptualizations. In other words, the intension of the concepts in A and B should be mapped to the intension of C's concepts
Unfortunately, this cannot be realized using only the conceptual relations specified in A and B for local tasks (for a specific context ). The methodological principle adopted here is that generic ontologies reused from the philosophical, linguistic, mathematical, AI literature must found the comparison of different intensions. Our approach may be called principled conceptual integration
3.1. For any set of sibling concepts in a taxonomy, the conceptual difference between each of them is inferred, and such difference is formalized by axioms that reuse the relations and concepts already in the library. If no concept is available to represent the difference, new concepts are added to the library
3.2. For any set of polysemous senses of a term, different concepts are stated and placed within the library according to their topic and to the available modules. ( Polysemy occurs when two concepts with overlapping or disjoint intended models have the same name .)
3.3. Often, polysemous senses of a term - as well as different 'alternative' concepts - are metonymically related. For example: process/outcome (as in inflammation ), region/object (as in body region ), etc. Alternatives must be properly defined by making it explicit the relationship between them: e.g. "has-product" for inflammation , "location" for body-region
3.4. When stating new concepts, the relations necessary to maintain the consistency with the existing concepts are instantiated. If conflicts arise with existing theories, a more general theory is searched which is more comprehensive. If this is impracticable, an alternative theory is created
3.5. Relevant integration cases . Since ONIONS requires the use of generic theories to axiomatize alternative theories, the integration of a concept C from an ontology O is performed by comparing C with the concepts D 1,…,n already present in the evolving ontology library L , whose ontology set M 1,…,n contains at least a significant subset of generic ontologies and the set of domain ontologies at that state in the evolution of L . The following cases appear relevant to the methodology:
3.5.1. C 's name is polysemous in O ( internal polysemy ). Iterate 3.2 ÷ 3.4
3.5.2. C 's name is homonym with the name of a D i . ( Homonymy occurs when both the intended models and the domains of two concepts with the same name are disjoint.) Homonyms must be differentiated by modifying the name, or by preventing the homonyms to be included in the same module namespace
3.5.3. C 's name is synonym with the name of a D i . ( Synonymy is the converse of homonymy and occurs when two concepts with different names have both the same intended model and the same domain. ) Synonyms must be preserved, or included in the set of lexical realizations related to the concept
3.5.4. C is subsumed by some D i in L , but it has no total mapping on any D j in L . The gap in L must be filled by adding C as a subconcept of D i
4. The library of generic, intermediate, and domain ontologies should be stratified , say domain modules should include intermediate modules - that should include generic modules - so that each set of modules can be plugged or unplugged from its more general set without affecting the coherence of the entire library
5. The source ontologies are explicitly mapped to the integrated ontology, in order to allow interoperability. The only admitted mappings are equivalent and coarser equivalent . Formally: for any source ontology SO and an ontology IO that is supposed to result (also) from the integration of SO , for any concept C i in SO , there is a D i in IO such that C i I = D i I (equivalence of possible interpretations), or there is a disjunctive concept ( or D i D j ) in IO such that C i I = D i I D j I (equivalence of possible interpretations to a disjunction of concepts – i.e. to a union of finer concepts)
5.1. Partial mappings must have been already resolved through the methodology: if any, some step in the integration procedure must be iterated
We created a Loom KB, containing, for each named concept, its direct super-concept (s), some annotations describing the quasi-synonyms , the gloss and the synset subject assignment, and its original numeric identifier in WordNet; for example:
:annotations ((subject animals)
(word |Equus caballus|)
(documentation "solid-hoofed herbivorous quadruped domesticated since prehistoric times"))
The synset Abstraction_1 includes both abstract entities , such as Set, Time, and Space, and abstractions such as Attribute, Relation, Quantity.
Abstraction_1 is glossed as "a general concept formed by extracting common features from specific examples”. Abstraction seems to be intended therefore as a psychological process of generalization. This meaning seems to fit the latter group of terms (Attribute, Relation, Quantity), but not the former, which would be considered as abstract under a different notion, namely not being extended in space/time .
Attribute , Relation , and Quantity are meta-level concepts, while Set , Time , and Space are object-level concepts.
Possession_1 is a role, and it includes both roles and types
Some hyponyms of Physical_Object are mapped to Feature
Abstraction_1 is the most heterogeneous Unique Beginner. It contains abstracts (Set_5), quality spaces (Chromatic_Color), qualities (mostly from the synset Attribute) and a hybrid concept (Relation_1) that contains abstracts, other entities, and even meta-level categories
Psychological_Feature contains both abstract entities (Cognition) and Events (Feeling_1)
Event_1, Phenomenon_1, State_1, Act are globally mapped to our Event category, although – by simply looking at their children – it seems quite hard to explicit any criteria to maintain the original distinctions
Following OntoClean, we have concentrated first on the so-called backbone taxonomy , which only includes the rigid properties. Formal and material roles have been therefore excluded from this preliminary work
An extreme heterogeneity appears evident:
Ex. Entity seems a “catch-all” class (Imaginary_place, Anticipation, Inessential, Location, Object, Causal_Agent, etc.)
Therefore, we also decided to exclude from the top-level cleaning those synsets sharing very few hyponyms (resembling “orphans”), like some of the above hyponyms of Entity
Names of anatomical morphologies are often polysemous:
Both a condition and the function that caused the condition ("inflammation", "ulcer", "fracture", "wound", "hyperplasia")
Both an object and the function that produced the object ("neoplasm", "hemorrhage")
Both an object O and the condition created in another object O' by O ("obstruction")
For example: " the fracture has been caused by a fall " vs. " the fracture is transverse "; " the obstruction occurred in the jejunum " vs. " the obstruction has been removed "
Conceptual analysis puts into evidence other issues concerning morphologies:
The dependence between a morphological condition, a function, and the related organ. For example, an "ulcer" (as a condition) of a stomach implies that the stomach embodies an ulceration function (an ulcer as a function)
The mereological import of morphologies: some are featured by an organ, some only by a part of an organ. For instance, an "ectopic heart" is wholly ectopic, but an "ulcerated stomach" is only partly ulcerated