The Semantic Web

The semantic web is a way to allow machine-interpretable knowledge to be distributed on the World Wide Web. Instead of just serving HTML pages that are meant to be read by humans, websites will also provide information that can be used by computers.

At the most basic level, XML (the Extensible Markup Language) provides a syntax designed to be machine readable, but which is also possible for humans to read. It is a text–based language, where items are tagged in a hierarchical manner. The syntax for XML can be quite complicated, but at the simplest level, the scope of a tag is either in the form , or in the form .

A URI (a Uniform Resource Identifier) is used to uniquely identify a resource. A resource is anything that can be uniquely identified, including individuals, classes and properties. Often URIs use the syntax of web addresses.

RDF (the Resource Description Framework) is a language built on XML, for individual–property–value triples.

RDF–S (RDF Schema) lets you define resources (and so also properties) in terms of other resources (e.g., using $subClassOf$, and $subPropertyOf$). RDF–S also lets you restrict the domain and range of properties and provides containers: sets, sequences, and alternatives.

RDF allows sentences in its own language to be reified. This means that it can represent arbitrary logical formulas and so is not decidable in general. Undecidability is not necessarily a bad thing; it just means that you cannot put a bound on the time a computation may take. Logic programs with function symbols and programs in virtually all programming languages are undecidable.

OWL (the Web Ontology Language) is an ontology language for the World Wide Web. It defines some classes and properties with a fixed interpretation that can be used for describing classes, properties, and individuals. It has built-in mechanisms for equality of individuals, classes, and properties, in addition to restricting domains and ranges of properties and other restrictions on properties (e.g., transitivity, cardinality).

There have been some efforts to build large universal ontologies, such as Cyc (www.cyc.com), but the idea of the semantic web is to allow communities to converge on ontologies. Anyone can build an ontology. People who want to develop a knowledge base can use an existing ontology or develop their own ontology, usually building on existing ontologies. Because it is in their interest to have semantic interoperability, companies and individuals should tend to converge on standard ontologies for their domain or to develop mappings from their ontologies to others’ ontologies.

Aristotelian Definitions

Categorizing objects, the basis for modern ontologies, has a long history. Aristotle [350 B.C.E.] suggested the definition of a class $C$ in terms of

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  Genus: a superclass of $C$. The plural of genus is genera.

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  Differentia: the attributes that make members of the class $C$ different from other members of the superclass of $C$.

He anticipated many of the issues that arise in definitions:

If genera are different and co-ordinate, their differentiae are themselves different in kind. Take as an instance the genus “animal” and the genus “knowledge”. “With feet”, “two-footed”, “winged”, “aquatic”, are differentiae of “animal”; the species of knowledge are not distinguished by the same differentiae. One species of knowledge does not differ from another in being “two-footed”. [Aristotle, 350 B.C.E.]

Note that “co-ordinate” here means neither is subordinate to the other.

In the style of modern ontologies, we would say that “animal” is a class, and “knowledge” is a class. The property “two-footed” has domain “animal”. If something is an instance of knowledge, it does not have a value for the property “two-footed”.

To build an ontology based on Aristotelian definitions:

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  For each class you may want to define, determine a relevant superclass, and then select those attributes that distinguish the class from other subclasses. Each attribute gives a property and a value.

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  For each property, define the most general class for which it makes sense, and define the domain of the property to be this class. Make the range another class that makes sense (perhaps requiring this range class to be defined, either by enumerating its values or by defining it using an Aristotelian definition).

This can get quite complicated. For example, to define “luxury furniture”, the superclass could be “furniture” and the distinguishing characteristics are cost is high and it feels soft. The softness of furniture is different than the softness of rocks. You also probably want to distinguish the squishiness from the texture (both of which may be regarded as soft).

The class hierarchy is an acyclic directed graph (DAG), forming a lattice. This methodology does not, in general, give a tree hierarchy of classes. Objects can be in many classes. Each class does not have a single most-specific superclass. However, it is still straightforward to check whether one class is a subclass of another, to check the meaning of a class, and to determine the class that corresponds to a concept in a person’s head.

In rare cases, the natural class hierarchy forms a strict tree, most famously in the Linnaean taxonomy of living things. The reason this is a tree is because of evolution. Trying to force a tree structure in other domains has been much less successful.