Organization
Section 1.1
Decidable 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.
Chapter 2 covers the requirements for the tutorial and describes the Protégé user interface.
Chapter 3 gives a brief overview of the OWL ontology language.
Chapter 4 focuses on building an OWL ontology with classes and object properties. Chapter 4 also describes using a Description Logic Reasoner to check the consistency of the ontology and automatically compute the ontology class hierarchy.
Chapter 5 describes data properties.
Chapter 6 describes design patterns and shows one design pattern: adding an order to an enumerated class.
Chapter 7 describes the various concepts related to the name of an OWL entity.
Chapter 8 builds on the Pizza tutorial from chapters 1 ‒ 7. This version has a few instances and property values already created. These can be used to show how to write rules, make queries, and set constraints using the tools discussed in later chapters.
Chapter 9 describes two tools for doing queries: Description Logic queries and SPARQL queries.
Chapter 10 introduces the Semantic Web Rule Language (SWRL) and walks you through creating SWRL and SQWRLTab rules.
Chapter 11 introduces the Shapes Constraint Language (SHACL) and discusses the difference between defining logical axioms in Description Logic and data integrity constraints in SHACL.
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with contributions from @gigster99 and @ldodds -
