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Knowledge is represented in Formal Concept Analysis as a formal context. This describes a binary relationship between a set of objects and a set of attributes of a domain.
Where
is a set of objects,
a set of attributes and
a binary incidence relationship between
and
with
Since formal contexts are a binary relationship they can be represented as cross tables. Here each object and attribute is represented as a row and a column respectively (Wille, 1982; see also Ganter, Stumme, & Wille, 2002)
Let’s take an example to illustrate formal concept definitions making use of the Solar system. Figure 1 shows the eight major planets in our Solar System with details of seven different properties. The table has the eight planet as rows and the eight properties as columns. A cross is used to mark the presence of a property against a planet. For example, the planets Jupiter, Saturn, Uranus and Neptune are considered to be gas giant planets. This is denoted in the table with crosses marked against each of the above planets for the property gas giant planet. The rows are known as extents and the columns are known as intents. A formal concept is defined as a pair of maximum of a set of extents and a set of intents. For the earlier example, we can also see that the four planets also have the property Has Some Moon checked. So the formal concept consisting of gas giants is defined as ({Jupiter, Saturn, Uranus, Neptune}, {Gas Giant, Has Some Moon}). Similarly, we can define a formal concept of planets that are gas giants and where the sun sets in the West. From Figure 1, we can find the following concept ({Jupiter, Saturn, Neptune}, {Gas Giant, Sun sets in the west, Has some Moon}). Here too the property Has some moon is a common property and is included as part of the formal concept. The planets Jupiter, Saturn and Neptune are the gas giant planets where the sun sets in the west. The planets mentioned above are the extent of this formal concept and the three attributes form the intent. A mathematical definition of Formal Concepts is given below.
Figure 1. A context about planets in our solar system (Krötzsch & Bernhard, 2009)
For a set of objects 
the set 
is defined as
Similarly, for a set of attributes 
the set 
is defined as
is a formal concept if 
and 
.