is some object in A that does not have that attribute. For computing purposes, a formal context may be naturally represented as a (0,1)-matrix K in which the rows correspond to the objects, the columns correspond to the attributes, and each entry ki,j equals to 1 if "object i has attribute j." In this matrix representation, each formal concept corresponds to a maximal submatrix (not necessarily contiguous) all of whose elements equal 1. It is however misleading to consider a formal context as boolean, because the negated incidence ("object g does not have attribute m") is not concept forming in the same way as defined above. For this reason, the values 1 and 0 or TRUE and FALSE are usually avoided when representing formal contexts, and a symbol like × is used to express incidence. Concept lattice of a formal context The concepts (Ai, Bi) of a context K can be (partially) ordered by the inclusion of extents, or, equivalently, by the dual inclusion of intents. An order ≤ on the concepts is defined as follows: for any two concepts (A1, B1) and (A2, B2) of K, we say that (A1, B1) ≤ (A2, B2) precisely when A1 ⊆ A2. Equivalently, (A1, B1) ≤ (A2, B2) whenever B1 ⊇ B2. In this order, every set of formal concepts has a greatest common subconcept, or meet. Its extent consists of those objects that are common to all extents of the set. Dually, every set of formal concepts has a least common superconcept, the intent of which comprises all attributes which all objects of that set of concepts have. These meet and join operations satisfy the axioms defining a lattice, in fact a complete lattice. Conversely, it can be shown that every complete lattice is the concept lattice of some formal context (up to isomorphism). Attribute values and negation Real-world data is often given in the form of an object-attribute table, where the attributes have "values". Formal concept analysis handles such data by transforming them into the basic type of a ("one-valued") formal context. The method is called conceptual scaling. The negation of an attribute m is an attribute ¬m, the extent of which is just the complement of the extent of m, i.e., with (¬m)′ = G \ m′. It is in general not assumed that negated attributes are available for concept formation. But pairs of attributes which are negations of