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Section 3.1
An OWL ontology consists of Classes, Properties, and Individuals.
OWL ontologies are an implementation of Description Logic which is aDecidable Subset
A decidable subset is a set of natural numbers for which there exists an algorithm
that can always tell whether a given number is in the set or not.
This algorithm will give a definite answer (yes or no) after a finite amount of time
for any number you test.
Examples:
- Any finite set of numbers.
- The set of all natural numbers.
- The set of prime numbers.
Non-examples:
- The set of Turing machines that halt (this problem is undecidable).
- Certain complex mathematical problems like Hilbert’s tenth problem,
which cannot be decided by any algorithm.
Key Points:
- If you can create an algorithm that always decides whether a number is in the set,
the set is decidable. - If no such algorithm exists, the set is undecidable.
- If a set is decidable, the set of numbers not in it is also decidable.
A class in OWL is a set, a property is a binary relation, and an individual is an element of a set.
Other concepts from set theory are also implemented in OWL such as Disjoint sets, the Empty set owl:Nothing, inverse relations, transitive relations, and many more.
An understanding of the basic concepts of set theory will help the user get the most out of OWL but is not required. One of the benefits of Protégé is that it presents an intuitive GUI that enables domain experts to define models without a background in set theory. However, developers are encouraged to refresh their knowledge on logic and set theory.
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with contributions from @gigster99 and @ldodds -
