Abstract: A computer-implemented method to capture and detect clusters in, or determined by, a set V of discrete digital data comprising; computing, from the set V, an abstract separation system ASS that consists of a finite set S, whose elements are called separations; of a predetermined transitive, antisymmetric and reflexive order relation ? on S; and of an order-reversing involution *: S?S, that is, a mapping s?s* with the property that, (s*)*=s and that r?s implies s*<r* for all r, s?S; predetermining a set of consistency requirements (CRs), that is, a set F of subsets of S; computing, from the ASS (S,?, *), one or more abstract tangles, that is, any set T?S that contains exactly one of each pair {s, s*} for s?S, and does not contain any of the forbidden configurations F?F as a subset; or determining that there is no abstract tangle; and determining that any abstract tangle T represents a cluster in, or determined by, the data set V.

Abstract: A method of mechanically identifying and distinguishing clusters of qualities amongst potential qualities of given objects. Also a computer-readable storage device having stored thereon instructions for carrying out such method. Moreover, a system for mechanical exploitation of a data set containing relations of objects each with at least one respective quality, each object being an element of a given set of objects, the qualities each being included in a given list of potential qualities.

Abstract: A computer-implemented method to capture and detect clusters in, or determined by, a set V of discrete digital data comprising; computing, from the set V, an abstract separation system ASS that consists of a finite set S, whose elements are called separations; of a predetermined transitive, antisymmetric and reflexive order relation ? on S; and of an order-reversing involution * : S?S, that is, a mapping s?s* with the property that, (s*)*=s and that r?s implies s*<r* for all r, s ? S; predetermining a set of consistency requirements (CRs), that is, a set F of subsets of S; computing, from the ASS (S,?, *), one or more abstract tangles, that is, any set T?S that contains exactly one of each pair {s, s*} for s ? S, and does not contain any of the forbidden configurations F ? F as a subset; or determining that there is no abstract tangle; and determining that any abstract tangle T represents a cluster in, or determined by, the data set V.