Chronological networks in archaeology: A formalised scheme

Highlights

• We present a new conceptual model of chronological networks in archaeology.

• We present a mathematical formalisation of chronological networks in archaeology.

• We propose algorithms for solving chronological problems in archaeology.

• We propose new software for modelling chronological networks.

• We propose a case study related to the Egyptian 26th dynasty.

Abstract

This paper proposes a new methodology for modelling chronological data in archaeology. We introduce the concept of “chronological network”, a flexible model for representing chronological entities, synchronisms between them, and other chronological constraints such as termini post/ante quem and duration bounds. We propose a procedure for checking the consistency of a chronological network and for refining dating estimates from the available synchronisms and constraints. We introduce ChronoLog, a chronology software application that allows users to build a chronological network interactively. The software automatically checks the consistency of the network and computes the tightest possible chronological range for each entity, within seconds. ChronoLog is freely available online at http://chrono.ulb.be.

Introduction

Our understanding of the ancient past often takes the shape of a network. Synchronisms between kings, historical eras, archaeological strata and ceramic types induce a complex web of interconnected chronological objects. An important aspect of such a web is the strong dependency among its components: a change at one end of the network can directly impact dates anywhere along the network. Changing a king’s regnal dates, for example, can directly affect the dating of an archaeological stratum containing objects bearing that king’s name. This can in turn affect the dating of ceramic types found in that stratum, and so on. Although chronological networks are frequently informally described in archaeological literature, they are often not explicitly recognised as such and, as a result, have never been fully formalised. This paper presents a formalised framework of chronological networks in archaeology. We first describe a conceptual model of chronological networks, featuring chronological sequences, upper/lower bounds on dates and durations, and several types of synchronisms (Section 2). This leads to a detailed mathematical model of chronological networks (Section 3). Based on this mathematical formalism, we introduce efficient algorithms for solving basic chronological problems. Two particular problems – consistency checking (i.e., verifying that the network features no contradictions) and tightening (i.e. computing the tightest possible chronological ranges for each date and duration) are of paramount importance. Readers not concerned with the details of mathematical modelling can skip Section 3, and move on to Section 4, which describes ChronoLog – software that facilitates construction of chronological networks, checks their consistency and provides tightened estimates of each boundary and duration, quickly and interactively. We illustrate the use of ChronoLog with a case study related to the Egyptian 26th dynasty (Section 5). Finally, Section 6 discusses future perspectives for both the model and the software implementation.

The question of representing and manipulating information about time has been long studied in the field of artificial intelligence, see for example the seminal works of Allen (1984, 1991). While some of the techniques we develop in Section 3 are related to these works (like the graph-based representation of the chronological constraints), the latter are very general and do not focus on needs related to archaeological data. Moreover, these earlier works are mainly concerned with the representation of the data, while we also present algorithms and software that directly address archaeological problems.

Allen’s early work (Allen, 1984) characterised 13 basic relations among temporal intervals. These relations were originally defined in the framework of temporal logic, but were later applied to archaeology by Holst (2004). The characterisation of chronological relations presented in this paper (Section 2.1) expands on Allen and Holst.

An interesting related work is that of Kromholz (1987), who proposed in 1987 to use off-the-shelf business-oriented computer programs to formalise archaeological chronology problems. These programs use typical models from the business world (PERT and Gantt charts) and rely on classical algorithmic methods (the co-called “Critical Path Method”) to analyse them and test different chronological hypotheses. Kromholz rightfully asked “how to deal with the immense quantity of data offered by every spadeful of earth we disturb” (Kromholz, 1987, p. 119) and we fully concur with his pioneering approach. His model differs from ours in several ways. To begin with, the data models are different. Ours allows us to model more diverse types of chronological constraints (see Section 2.1). Furthermore, the two approaches do not address exactly the same questions and rely on totally different algorithmic techniques. Finally, the technique proposed by Kromholz uses commercially-produced business-oriented software not originally intended for archaeology, which requires the user to shuttle between the terminologies of two widely different disciplines. The solution proposed in this paper is aimed at archaeologists’ needs, with a data model consisting of more archaeologically-meaningful basic elements.

Our work can also be compared to more traditional formal approaches for stratigraphic analysis, such as the frequently-used Harris matrix (Harris, 1979) or the partial order scalogram analysis of relations by Sharon (1995). These approaches, however, deal only with relative chronology, while our approach considers both relative and absolute chronology aspects in a unified model. As such it comes close to the approach of Desachy (2016), who augments the traditional Harris matrix approach by adding to it, as in our model (see Section 2 below), upper and lower bounds on the start date, end date, and duration of each stratigraphic unit. Our approach features an additional set of possible synchronisms, a more powerful algorithmic tool for detecting inconsistencies and new algorithms for computing tight time and duration ranges (see Section 3).

The work closest to ours is that of Falk (2020), who implemented a chronological tool called Groundhog (see http://www.groundhogchronology.com/), which allows building of chronological networks and testing them for internal contradictions. His approach differs from ours in several aspects. First, our model allows for more diverse types of chronological constraints (see Section 2). Second, Falk’s approach relies on exhaustive search, by generating all possible combinations of dates, thus yielding exponential-time algorithms, whereas we employ a more efficient approach, using polynomial-time algorithms (see Section 3); this means that Falk’s approach is unlikely to be able to handle networks of large sizes in short processing time. Our technique can scale and handle networks with several hundred chronological constraints in less than a second, allowing for a truly interactive experience for the user (see Section 4.3.2).

Other formal approaches to archaeological chronology, not directly related to ours, rely on fuzzy logics (Niccolucci and Hermon, 2015), aoristic analysis (Crema, 2012), and evidence density estimation (Demján and Dreslerová, 2016). For the Bayesian approach in radiocarbon, and its relation to ChronoLog, see Section 4.3.1.