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

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.