"An ontology is a formal and explicit specification of a shared conceptualization" (Thomas Gruber).
"What is there? Everything" (Quine)
"To be is to be the value of a variable" (Quine).
"There is no entity without identity" (Quine).
Definition of ontology
In computer science, an ontology is a set of concepts and relationships between them to model, ground, describe and represent a domain of knowledge. The most usual synonym for the term "ontology" is "conceptualization".
There are many definitions of ontology in the literature:
"An instrument that defines the basic terms and relationships from the vocabulary of an area, as well as the rules for combining these terms to define extensions of the vocabulary [Neches, 1991].
"An ontology is a database that describes general concepts or about a domain, some of their properties, and how the concepts relate to each other" [Weingand, 1997].
"An ontology is an explicit representation of a cognitive conceptualization, i.e., the description of the relevant knowledge components in the modeling domain" [Breuker, 1999].
The definition of ontology in computer science that is considered the most appropriate was the one proposed by Thomas Gruber is his article "Toward Principles for the Design of Ontologies Used for Knowledge Sharing": "An ontology is a formal, explicit specification of a shared conceptualization" [Gruber, 1995].
In this definition, "conceptualization" refers to a framework or model of a domain from which relevant concepts are identified. "Shared" refers to the fact that the knowledge captured by the ontology must have the consensus of a community. "Formal and explicit specification" means that a formal language of representation must be used to make the concepts used and their relationships explicit.
Historically, ontologies have emerged from metaphysics, a branch of philosophy that deals with the transcendent nature of reality, the hidden essence behind all that exists. The term "Ontology" comes from the Greek ontos (being). Computational ontologies can be considered as a kind of "applied philosophy".
Philosophers have long debated possible methods for discovering, describing, and constructing ontologies. In contrast, computer scientists have built ontologies at the practical level with little debate about their theoretical foundations.
Ontologies have become a common field of interest in many fields: software engineering, knowledge engineering, knowledge representation, knowledge bases, artificial intelligence, semantic web, natural language processing, and so on. The reason for so much interest lies in the fact that ontologies constitute a meeting point between the human mind and the machine.
Characteristics of ontologies
There is no single way to ontologically model a domain. It depends on the application. A domain can be interpreted and represented in many ways, by means of different ontologies, depending on the intended purpose. Any ontology represents a certain worldview or paradigm of a domain. An ontology should not contain everything that is known about the domain, it should only contain what is necessary for the application.
The ontology of a domain allows to establish a firm base to capture the knowledge of that domain. It makes explicit the conceptual foundation of a domain, its structure and relationships. It separates descriptive from operational knowledge, and provides the foundation for reasoning and inferring in the domain.
A domain ontology must be clear, objective, coherent and extensible or generalizable.
Ontology models are more robust and deeper than information-based models. Ontology should be the foundation for information structuring.
A distinction must be made between ontology and knowledge base. Ontology describes the concepts and their relationships. The knowledge base describes the instances, the data.
The component concepts of an ontology are not formally definable. They are the conceptual axioms of the domain, from which the domain is modeled.
Ontologies favor the generalization of a domain. And when there are common concepts or a common conceptual model they facilitate interconnection between particular domains and interoperability between software systems.
The ontological approach is top-down: from the general (concepts) to the particular (properties and instances). In general, from the deep to the superficial, from the general to the particular.
There are generic, domain and representational ontologies. Generic ontologies are formed by abstract concepts. Domain ontologies are based on concrete concepts. Representational ontologies are conceptualizations that underlie knowledge representation formalisms, so they are also called "meta-ontologies", i.e. ontologies that refer to ontologies.
Components of an ontology
The components of a domain ontology are:
Classes. They represent the concepts of the domain.
Elements or instances of the classes.
Properties of the elements of the classes.
Axioms. They are general relations between classes and/or properties.
Specific relationships between classes, properties and domain elements. These relationships can be rules, processes, events, functions, etc.
Characteristics:
The definition of an ontology in a domain involves the creation of a vocabulary to define classes and properties.
Classes are the building blocks of an ontology. Classes can be disjoint or not, depending on whether or not they have common elements. The granularity of an ontology refers to the number of classes in the ontology.
The classes of an ontology are related and form a structure. This structure can be hierarchical, non-hierarchical or mixed (partially hierarchical). The hierarchy is articulated on the relation "is a/an": a class A is a subclass of B if each instance of B is also an instance of A. The subclass relationship is transitive.
A class can have several subclasses. Subclasses inherit the properties of the class to which they belong, but there may be additional properties specific to each subclass. A class can be a subclass of several classes and have multiple inheritance.
A property can have subproperties. An element can have subelements. In short, there can be different hierarchical levels in the components of an ontology.
Concepts are often fuzzy, without a perfectly defined boundary. For example, a chair may have properties (height, number of legs, etc.) on the boundary with an armchair. Classes, on the other hand, must be perfectly defined.
There is also a fuzzy boundary between class and property. For example, "red wine" can be considered a class, or consider that there is a class called "wine" with the property of being red, white or rosé.
In an ontology there are primitive and derived concepts. A primitive concept is one that cannot be defined by other concepts. A derived concept is one that can be defined by primitive concepts.
Properties can be intrinsic or extrinsic. An intrinsic property is one that always belongs to the elements of a class. An extrinsic property is one that does not belong to its essence. For example, the property of a wine to be red is intrinsic. The property of a wine to be cold is extrinsic.
Properties are subject to constraints: the type of value, its cardinality (one or more values), the range of possible values, the default value, etc. In addition, the value (or values) of a property of a class may depend on one or more values of other properties of the same or different class.
The ontological problem
In order to make the world comprehensible and to give meaning to everything that surrounds us, human beings conceive and postulate all kinds of entities:
Concrete, such as this tree, this table, etc.
Abstract, such as friendship, compassion, etc.
Physical, such as atoms, dark energy, dark matter, gravitational waves, the planet Vulcan, etc.
Biological, such as genes, organs, tissues, etc.
Universal, such as animal, man, etc.
Mental (or ideal), such as ideas, thoughts, concepts, etc.
Mathematical, such as numbers, sets, geometric figures, vectors, matrices, etc.
Imaginary, like Don Quixote, Faust, etc.
Spiritual, such as God, angels, etc.
The ontological problem has several aspects. Some of them are:
There are entities that are speculative, with supporters and detractors of their existence. Some are eventually proven to exist (such as atoms or gravitational waves). Others are finally proven not to exist (such as the planet Vulcan). There are also competing theories that postulate different entities in a given domain.
The problem of the existence of universals, which do not refer to any concrete entity. If they exist, what is their nature? Do they exist in concrete entities or do they exist independently of them? Are they just names? An analogous problem is that of abstract entities.
The problem of naming entities that do not exist, such as nothingness. Nothingness is a contradictory concept. On the one hand, we are referring with a name to something, so that something must exist (otherwise we could not give it a name). And on the other hand, according to its meaning, it does not exist.
The problem of mental entities: Do they really exist or are they just mere neuronal processes?
The problem of language in general. What is the ontological level of language?
The problem of definite descriptions, a problem posed by Russell exemplified by the sentence "The present king of France is bald." This sentence is referring to an entity that does not exist, and yet an attribute (being bald) is being assigned to it. How can an attribute be assigned to something that does not exist?
The problem of the possible existence of primary or fundamental entities, from which all the others would derive. If they exist, they would have to be of supreme level of abstraction. And the problem of the relation of these primary entities with the mathematical entities, which are also abstract. Are they the same entities?
The problem of representational ontologies. For example, those associated with formal languages in general and ontology languages in particular.
The problem of imaginary and possible entities. Do these entities exist in some higher dimension?
Quine has studied the ontological problem and has launched several ideas:
The ontological principle has a very simple formulation and a very simple answer: "What is there? Everything." That is, there is no universal, general or absolute ontological problem. The ontological problem is relative: it only affects concrete particular entities, each of which presents a different problem.
He advocates not using names to refer to entities that we do not know whether they exist or not, because if we assign names to them then we are assuming their existence. To avoid this paradox (which he calls "Plato's beard"), he proposes to use only predicates. With them we can deny the existence of an entity that has a particular property.
There is a "semantic ascent" according to which, instead of talking about things, we focus on the language with which we talk about things in order to avoid the problem of the existence of things.
The "ontological commitment" is an attitude according to which we accept the existence of some entities as real, as for example, in mathematically formalized scientific theories. It states that "To be is to be the value of a variable". He means that we assume that a variable is a real entity and the origin of reification and, therefore, of ontology.
He states that "There is no entity without identity". Every entity must have identity in order to be distinguishable from others. In the case that an object is the value of a variable it is susceptible to be identified within the context of a theory.
For Plato, there are some ideal entities that reside in a higher realm independent of the real world, the world of Ideas or Forms, which are the truly real entities, and which manifest themselves imperfectly in the sensible world.
For Aristotle, everything must be based on first principles or first causes. He sought the being of things, not by their accidents, but by their "substance," the ultimate substratum and foundation of all that exists.
For the neopositivists of the Vienna Circle, every metaphysical entity is meaningless because it cannot be experientially verified.
For the Bourbaki group, mathematical entities are structures, relations between elements whose nature is indifferent. There are three types of mother structures: algebraic, order and topological. From them new structures can be generated, which have a hierarchical structure. This structuralist conception of mathematics has been generalized to patterns of structures by Michael Resnik and Stewart Shapiro [Resnik, 1977].
The epistemological problem
Epistemology is the study of the acquisition of knowledge. The epistemological problem also has many aspects, among them: How do we obtain knowledge? Do we learn through sensible experience or by reason? Does intuition intervene? How does the mind relate to reality? How is it possible that knowledge can be transmitted from one mind to another through language? How does objective and subjective knowledge relate? Is there a priori knowledge?
Upper Ontologies
In computer science, an upper ontology −also known as "universal ontology", "top level ontology" and "foundation ontology"− is a hypothetical set of concepts of supreme level of abstraction common to all domains of knowledge. These concepts are also called "semantic primitives" or "primary concepts".
There has been much discussion about the existence or not of a universal ontology. If it did exist its advantages would be enormous:
Every particular ontology would be the result of a certain combinatorics of the universal ontology. Therefore, all ontologies of particular domains would be connected through the universal ontology.
It would provide a standard system of knowledge representation. And a means to integrate heterogeneous knowledge coming from different fields.
If there were also a language based on a universal ontology, it would be a universal language, a standard language for the formal sciences.
Historically there have been numerous attempts to establish a universal ontology, but none has gained general acceptance to be considered de facto standard. The main reason has been its complexity: too many primary concepts and too many relations between those concepts, a complexity similar to that of human language or even higher because of the added difficulty of having to learn a syntax. There are higher ontologies that consist of thousands of elements, including classes, properties and relations.
MENTAL, an Ontology Definition Language
Ontology vs. Epistemology
Ontology studies the essence of reality, its structure or deep essence. Epistemology studies the deep nature or essence of knowledge. But ontology and epistemology share the same essence, which are the archetypes of consciousness. Knowledge is created and articulated on these archetypes.
For Kant, the essence of reality (the noúmeno) is unknowable. We can only know the phenomena, the superficial, what is perceived by the senses. The boundary between the superficial and the profound resides in the primary archetypes.
According to the principle of descending causality, the deep nature must necessarily be abstract, which manifests itself in the concrete. There are many abstractions, but there are universal or supreme abstractions that ground all others. They are universal because they make no reference to any particular entity, but to a class or categories of entities. They are a finite set of fundamental or primary concepts, also called "universal semantic primitives". These concepts manifest themselves in human language in the form of a semantic grammar, which is constituted by the possible relations between the primary concepts.
The ontological problem is the problem of the grounding of reality, and the epistemological problem is the problem of the grounding of knowledge. Both foundations are based on supreme or universal abstractions, which are universal semantic primitives, primary archetypes, and philosophical categories.
The epistemological problem is the problem of knowing knowledge, which is impossible. To achieve this, one must place oneself in a higher perspective, the limit of which lies precisely in the primary archetypes. In this sense, the epistemological problem is the same as the ontological problem.
According to Kant's "Copernican revolution," the structures of the human mind condition knowledge and experience. But what conditions and grounds everything are not the mental structures, but the primary archetypes common to the internal and external world.
Plato's ideal world of Forms is a world of static and independent abstractions, and is not a world that can be reduced to a single set of abstractions or universal Forms. Instead, for Jung, the primary archetypes is a reduced set of primary archetypes, which are dynamic in nature and are not autonomous, but interdependent.
Inner (psychic) world and outer (physical) world share the same primary archetypes. Deep or supreme ontology is based on universal abstractions. Epistemology is the manifestation of that universal ontology in the human mind. So ontology and epistemology share the same essence, the same foundations, the same primary archetypes. Nature follows the principle of maximum simplicity.
MENTAL, a universal ontology-epistemology
In the same way that the fish is not able to perceive water, we do not perceive primary concepts because they are so simple that we are not aware of them because they are part of all reality, internal and external. That is why, paradoxically, it is so difficult to find the simplest, the most fundamental, because we are immersed in them. Simplicity, abstraction, truth and the fundamental are concepts that go together.
Everyone possesses ontologies by which they conceptualize the world around them. These ontologies are not explicit. For example, when we hear or read the word "bicycle," we automatically imagine a generic bicycle and create for ourselves a mental representation with intrinsic properties (two wheels, handlebars, saddle, etc.). The soul imagines, the mind conceptualizes, the consciousness relates, including the relationship between soul and mind. And the mind conceptualizes thanks to the consciousness. And in every relation the primary archetypes are involved (or underlie). That is why we call the primary archetypes "archetypes of consciousness".
At the computational level, ontology and epistemology are based on primary archetypes, which are concepts of supreme simplicity and generality. With MENTAL, the development of ontologies is made simpler and clearer.
MENTAL provides a universal ontology-epistemology:
It is an ontology because it deals with concepts and their relationships. It is universal because it is applicable to many domains, providing them with:
A common semantic basis.
A way of integration, relationship and communication that dilutes their borders.
A generic conceptual framework of reference.
A semantic standardization.
A universal ontology that grounds particular ontologies.
It is a universal language, a lingua franca that allows expressing ontologies and epistemologies. They are universal semantic primitives, primary archetypes and philosophical categories.
Domains have ontologies, and languages are also based on ontologies. In MENTAL, the ontology is universal, including the representational ontology. It is based on primary archetypes that are common to everything because everything has the same underlying conceptual structure. That is why the world is intelligible. All ontologies reduce to fundamental ontologies, which are the degrees of freedom of all internal and external reality.
The universal ontology is the primary archetypes. The manifestations are the concrete expressions. This makes it possible to differentiate between being and existing. The primary archetypes are being and their manifestations are existing. Existence is based on being. This generalizes and qualifies Quine's conception: the variables are really the primary archetypes, and the expressions are the values, which represent their identity.
The relations between primary concepts are realized through the primary concepts themselves. At the linguistic level this implies that structural semantics is equal to lexical semantics.
It is a symbol-based language, to transcend and be independent of any concrete human language.
An example of ontology
An ontology about Painting:
Classes: Paintings, Painters, and Museums.
Relationships:
Painting-Painter (a painting has an author, the painter).
Picture-Museum (a picture is in a museum).
These relationships are 1:1. The inverse relationships Painter-Paintings and Museum-Paintings are 1:n (1 to several).
Picture-Museum relationship. This is done by means of the Museum function, which establishes a correspondence between each painting and the museum where it is located:
In this example we can see the difference between ontology and knowledge base. In the ontology, classes and generic relationships between classes are defined. In the knowledge base the instances of classes and their concrete relationships are defined.
The defined ontology and knowledge base could be extended. For example, new classes could be defined, such as: the nationality of the painters, the city and country where each museum is located, etc. And ask questions such as: the paintings of a painter that are in a certain country, the painters of a certain nationality, etc.
In addition to the query, one could do the maintenance of classes and relations:
Add element x to class C:
( C = {C↓ x} )
Remove element x from class C:
( C = C/(x=θ) )
Replace element x of class C with element y:
( C = C/(x=y) )
Addenda
Ontology languages, systems and methodologies
To represent ontologies it is very important to have a formal language. There are several ontology or knowledge representation languages, among them:
CycL. It is the ontology language of the Cyc project. It is based on first-order predicate logic with some higher-order extensions.
DAML. DARPA's Agent Markup Language.
F-Logic. Frame Logic. Ontology language to represent knowledge.
Gellish. It is a formal conceptual modeling language extensible by rules.
IDEF5. Integrated Definition for Ontology Description Capture Method. It is a method for modeling ontology oriented to software engineering.
KIF. Knowledge Interchange Format. It is based on first-order logic using S-expressions as syntax. An S-expression (or symbolic expression) is a notation for representing data structures in the form of a tree. It is preferably used in the Lisp language.
OIL. Ontology Inference Layer.
OWL. Web Ontology Language. Language for defining ontologies oriented to the standard web and the semantic web.
RIF. Rule Interchange Format. It is a part of the semantic web infrastructure.
SHOE. Simple HTML Ontology Extensions.
Currently, organizations and entities that develop ontologies mainly use the OWL language, a generic language for representing ontologies, but especially oriented for the Semantic Web.
There are also different methodologies for the implementation of ontologies, such as Methontology and On-To-Knowledge.
There are several software systems to implement ontologies such as Protégé, Ontolingua and Chimaera, Annotea, OrtoWeb, SchemaWeb. Protégé is one of the most known and used. With it you can easily create classes, class properties, create instances, etc., all through a friendly user interface. It has its own internal ontology language, but also allows working with RDF and OWL.
Examples of superior ontologies
We can highlight the following:
CIDOC Conceptual Reference Model (CRM).
COSMO (COmmon Semantic MOdel).
Cyc (abbreviation of "Encyclopedia").
DOLCE (Descriptive Ontology for Linguistic and Cognitive Engineering).
GFO (General Formal Ontology).
GUM (Generalized Upper Model).
OntoUML. It is an extension of UML to define ontologies. It is based on UFO (Unified Foundational Ontology).
PROTON (PROTo ONtology).
SUMO (Suggested Upper Merged Ontology).
UFO (Unified Foundational Ontology).
UMBEL (Upper Mapping and Binding Exchange Layer).
WordNet.
YAMATO (Yet Another More Advanced Top Ontology).
OWL (Web Ontology Language)
OWL is the W3C (World Wide Web Consortium) standard language for defining ontologies on the semantic web. Actually, the language should be called WOL, but it is spelled OWL for 3 reasons: 1) because it is an easier acronym to pronounce in English; 2) because it means "owl"; 3) by reference to "One World Language", an ambitious knowledge representation project (with its associated anthology) from the 1970's by Bill Martin that was intended to be a universal language to represent the meaning of natural language.
OWL is based on two principles: 1) the meaning of a language concept is the totality of the other concepts related to it; 2) on the existence of deep relationships between the representation of knowledge (on the one hand) and the structure and metaphors of natural language (on the other).
Features:
Allows you to define classes, properties, equivalent classes, disjoint classes, Boolean combinations of classes, constraints, logical statements and reasoning systems.
It is a logical language, which implements deductive reasoning. It is based on descriptive logic, a subset of predicate logic oriented to knowledge representation.
It is a language built on top of RDF and RDFS and encoded in XML. But it adds more vocabulary to describe classes and properties and relationships.
Allows you to define properties of properties (whether they are transitive, inverse, unique, etc.).
Allows to define automatic agents.
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