The Qualitative Algebras library

As we have noted, each algebra is represented by a XML file which contains the basic relations and the operations over the algebra.

An extern DTD (Document type definition) is used to define the legal building blocks of an XML document defining a Qualitative Algebra (the Qualitative Algebra DTD). It defines the document structure with has list of legal elements. Based on this DTD, we have defined ( and we can define again) XML files containing qualitative algebras. These files can be used by the tools of QAT. A qualitative algebra XML file is composed from several parts:

• The first part contains general information about the algebra (its name, the number of basic relations, its arity and comments about this algebra).
• The second one contains the definitions of the basic relations of the algebra. Each basic relation is defined by its id, its short name, its full name and a comment.
• The third part contains the definitions of the operations on the algebra. There are three operations:
  • the permutation,
  • the rotation,
  • the composition.
  Generally, an algebra equipped with the three operation is a relation algebra.
• The last part contains the diagonal elements.

For understanding this representation, we propose an elegant graphic interface using the java applet. For running the interface you should have java 1.5 on your machine (Go to http://java.sun.com/ to download and install Java).

You can see the XML definition of the algebra by clicking on the name of the qualitative algebra. You can also see the algebra ( its basic relations and its operations) in an graphic interface by clicking on the corresponding icon.

• RCC5Algebra
• MultiPointAlgebra
• CardinalDirectionAlgebra
• INDUAlgebra
• RCC8Algebra
• IntervalAlgebraAbstraction
• IntervalAlgebra
• CyclicIntervalAlgebra
• CyclicPointAlgebra
• PointAlgebra
• RectangleAlgebra

last update: 15 jan. 2006.