Using a topological approach allows overcoming the problems mentioned by
Koussoulakou and Stylianidis ( 1999 ) (see Sect. 2.1 ) New phases can be added
without causing problems whether it involves phases that fill gaps (3) or appear
within other phases (4), since only the topological relation in the topological com-
plex changes. The imperfect knowledge on (1) or changes of (2) begin and end
dates do not pose problems, as these are presented by topological nodes, and thus,
have not a fixed position in time. So, future changes of these dates will mostly not
affect the nodes and the structure of the topological complex (cf. spatial topology).
Likewise, issues (5) and (6) regarding the (re)assignment of a phase do not set a
problem. In both cases only an 'update' of the database or information is needed.
Moreover, the topological structure of the site phasing may meet the need,
pointed out by Green ( 2011 , p. 38), for multiple temporalities and non-linear
time representation. This need results from the sceptical points of view on phas-
ing and chronology as reflected by Lucas ( 2005 , pp. 9-10). The multiplicities at
the TM_Edge associations Termination and Initiation (Fig. 4 ) allow having non-
linear topology (NBN 2005 , p. 15). This means that different edges could share a
node. The NBN EN ISO 19108:2005 standard (NBN 2005 , p. 15) notes that this
can occur in two situations: (i) temporal characteristics of different objects are
represented or (ii) different temporal characteristics of the same object are repre-
sented. This allows, for example, that there are two initial phases (e.g. two cultural
groups), but only one continues in the future, while the other tends to extinguish.
Furthermore, it is worth mentioning that each site phase may have a 3D spatial
extent. This extent could be conceived of as a bounding box of all the excavation
objects having the same value for the site phase time.
The fourth temporal category, the stratigraphic time, is related to the deposi-
tion layer in which the object was found. This temporal characteristic bears resem-
blance to the previous category, the site phase. The same decisions could be made,
thus resulting in a TM_Edge representation for the single excavation objects.
Although defining one stratigraphic time for the whole site does not make much
sense, the TM_TopologicalComplex which is made up of all the object's strati-
graphic time TM_Edges will provide information on the objects' relations on the
site. The three relationships that can occur in a Harris matrix ( Sect. 2.2 ) are still
possible in this topological representation. First, the unlinked relationship is real-
ized by an edge, which does not share a node with another edge (Fig. 8 a). Second,
the later and earlier than relationships are possible by the edge connections, thus
by a shared node (Fig. 8 b). Third, an equivalence should result in two edges with
the same begin and end nodes (Fig. 8 c). Moreover, one could argue why not to
implement the stratigraphy as a temporal ordinal reference system. This is not a
decent option, since the stratigraphy in archaeological context is site-specific
and not a general succession or reference frame like the geological time scale.
Likewise for the previous category, the stratigraphic time may have a 3D spatial
extent as well.
The fifth temporal characteristic that can be assigned to an archaeological
object is the archaeological time. This temporal path is described by Katsianis
et al. ( 2008 ) as 'cultural temporal categorization' which means that a reference to