Sets, Graphs, and Things We Can See: A Formal Combinatorial Ontology for Empirical Intra-Site Analysis

J. Scott Cardinal
2019 Journal of Computer Applications in Archaeology  
Introduction A fundamental aspect of archaeological work is identifying patterns within a site of interest. The data most typically used to identify interpretable patterns are derived from our unit locations and stratigraphic levels, section profiles, numerous maps and detailed plans in addition to any artefacts collected. This information constitutes the empirical archaeological record -the physical, observed, measured, counted, and mapped samples from which we will build, by inference, all
more » ... sequent analyses and interpretations of the site. The archaeological record, however, is inherently both incomplete due to preservation and sampling and represents a convoluted final product of various transformations through site formation processes. With every subsequent transformation, the original deposit and context become somewhat more obscured. As we proceed through from excavation to interpretation, each step of the archaeological process entails a certain increase in abstraction from those initial empirical data. Archaeologists commonly expect, due to this incomplete nature of archaeological materials, that our inferences will reflect a certain amount of necessarily interpolated and extrapolated conclusions. Thus, we infer patterns from both the consistencies and the discontinuities between and among the data of the archaeological record. Each interpretative step we take away from the empirical data leads to an aggregation of further inferences. Such abstractions also, necessarily, involve a corresponding degree of information loss as particulars are subsumed into generalizations. The uncertainty introduced by moving incrementally further from the empirical basis of our data underscores the most difficult and pertinent question for interpreting the archaeological record -how can we show that our inferences, inasmuch as they are based on that empirical record, are correct? In other words, are we reasonably certain that we've correctly identified which samples belong to which contexts? Can we demonstrate that our assemblages are, in fact, related? How can we provide stronger evidence to support whether our samples are truly associated? Is there a way to penetrate the intervening layers of noise, untangle the cumulative transformations of postdepositional processes, and get a glimpse of the site as it was originally? At the core of it, the problem is that the analyses of spatial and temporal patterns of interest are derived from the underlying structure of relationships between those empirical samples, rather than from the underlying spatiotemporal structures and processes of the site itself. When we speak of the "integrity" of a site, or its "stratigraphic integrity", what is really at question is whether there is a clear and supportable chain of inference from the empirical excavated samples backwards through to the site's formation processes and their interpretive significance. A critical aspect of analysing an archaeological site is identifying the network of relationships between the things we find and the locations where we find them. These associations are typically determined by a combination of quantitative analyses and the professional knowledge and intuition of the archaeologist, but where exactly is the boundary between what is truly empirical field data and what is inferred through our prior knowledge and field methods? How can we best support those inferences? This paper is a critical evaluation of that boundary to firmly ground, as much as possible, a quantitative analysis on only that which we can directly observe -the thing and its location -and derive associations from that basis alone. To do so, the approach described here relies on a combination of set and graph theories rather than statistical or spatial methods. This revised ontology allows a formalization, in combinatorial terms, for describing an underlying structure to contexts and assemblages that suggests a clear association between archaeological site analysis and a well-studied class of set and graph covering problems. This, in turn, points towards potential algorithmic solutions for a more holistic parsing of the total relationships between sites, contexts, assemblages, proveniences, and artefacts.
doi:10.5334/jcaa.16 fatcat:l6gbhdcnlbcsvatxjsbfd2ucim