A retrieval model is embedded in a universe of objects. An object
is a 2-tuple
, where
is the object's unique id, and
is
the object's unique representation. The exact definition of representation depends
on specific retrieval tasks (Kulyukin 1999a; Kulyukin 1999b). The universe in which
M is embedded is the set of all objects, and is denoted by
. The finite
set of objects retrievable by M is denoted by
. The set
contains the
ids of objects in
. Since there is a bijection between
and
,
when the context permits, objects are referred to by their ids. M's primitives are
called tokens. The precise definition of a token depends on the context (Kulyukin
1998a; Kulyukin 1998b). Tokens can be keywords, keyword collocations, nodes in a semantic
network, etc. The set of all possible tokens is denoted by
.
If is M's set of representations, M's representation
function is
. If
,
. The token weight
function
assigns weights to tokens in objects. The object similarity function
computes the similarity between two objects in
. The rank function
imposes an ordering on
's objects. The rank of
with respect to
is denoted by
. If
, then
, and
. Thus, the
ranking of objects is determined by
and their initial ordering in
.
A retrieval sequence returned by M in response to is denoted by
,
and is a permutation
of the ids of objects in
such that
.
Let
and
.
and
are equivalent
under ranked retrieval (
) iff
=
,
,
,
... ,
,
,
,
=
,
,
,
... ,
,
,
, and
.