Soergel, D.: Mathematical analysis of documentation systems : an attempt to a theory of classification and search request formulation (1967)
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- Abstract
- As an attempt to make a general structural theory of information retrieval, a documentation system (DS) is defined as a formal system consisting of (a) a set o of objects (documents); (b) a set A++ of elementary attributes (key-words), from which further attributes may be constructed: A++ generates A; (c) a set of axioms of the form X++(x)=m (m¯M, M a set of constant connecting attributes with objects: from the axioms further theorems (=true statements) may be constructed. By use of the theorems, different mappings O -> P(o) (P(o) set of all subsets of o) (search question -> set of documents retrieved) are defined. The type of a DS depends on two basic decisions: (1) choice of the rules for the construction of attributes and theorems, e.g., logical product in coordinate indexing; links. (2) choice of M; M may consist of the two constants 'applicable' and 'not applicable', or some positive integers, ...; Further practical decisions: A++ hierarchical or not; kind of mapping; introduction of roles (=further attributes). The most simple case - ordinary two-valued Coordinate Indexing - is discusssed in detail; o is a free distributive (but not Boolean) lattice, the homographic image a ring of subsets of o; instead of negation which is not useful, a useful retrieval operation 'praeternagation' is introduced. Furthermore these are discussed: a generalized definition of superimposed coding, some functions for the distance of objects or attributes; optimization and automatic derivation of classifications. The model takes into account term-term relations and document-document relations. It may serve as a structural framework in terms of which the functional problems of retrieval theory may be expressed more clearly
