Introduction to Concept Lattices

Let us observe that there exists a 2-sorted which is strict and non empty and there exists a 2-sorted which is strict and non quasi-empty. Let us observe that there exists a 2-sorted which is strict, empty, and quasi-empty. We consider ContextStr as extensions of 2-sorted as systems 〈 objects, attributes, an information 〉, where the objects and the attributes constitute sets and the information is a relation between the objects and the attributes. Let us note that there exists a ContextStr which is strict and non empty and there exists a ContextStr which is strict and non quasi-empty. A FormalContext is a non quasi-empty ContextStr. Let C be a 2-sorted. An object of C is an element of the objects of C. An Attribute of C is an element of the attributes of C. Let C be a non quasi-empty 2-sorted. One can check that the attributes of C is non empty and the objects of C is non empty. Let C be a non quasi-empty 2-sorted. Observe that there exists a subset of the objects of C which is non empty and there exists a subset of the attributes of C which is non empty. Let C be a FormalContext, let o be an object of C, and let a be an Attribute of C. We say that o is connected with a if and only if: