This document discusses using Allen temporal operators to model stratigraphic relationships in archaeological analysis. It summarizes the key temporal relationships identified by Allen that are useful for modeling stratigraphy, including before, meets, overlaps, during, starts and finishes. The document also discusses issues with inconsistent standards for digitally archiving stratigraphic data and relationships, and the need for standards to make this fundamental archaeological data more reusable. Finally, it calls for international conventions on stratigraphic recording and analysis to facilitate understanding and communication across disciplines.

1. Space-Time in the Matrix and
Uses of Allen Temporal Operators for Stratigraphic Analysis
Presented by
Keith May @Keith_May
Keith.May@HistoricEngland.org.uk
Hubble Telescope view
of the Carina Nebula
showing star birth
https://esahubble.org/images/heic0707a/
“ Stratigraphie
est né libre, et
partout il est
dans les fers. “
“Stratigraphy is
born free, and is
everywhere in
chains” - KM,
with thanks to
J-J Rousseau

2. 1. Introduction & Background to The Matrix project
2. Conceptual Modelling uses of Allen Operators for
• Stratigraphic Analysis
• Temporal Relationships
• Chronological Modelling
3. Matrix project Methods: Archaeological Process & Data Modelling
4. Matrix project Methods: Digital Data & Stratigraphic Standards
5. Experiences from Re-use of digital stratigraphic data
6. Conclusions & Challenges
Overview of presentation

3. With thanks to CRM SIG - M. Doerr et al
Categories/
Terms/KOS
Who
Where
Names/
Identifiers
Activities/
Events
Documentation
E73 Information Objects
What
Timespan
When
CIDOC CRM ISO 21127:2014
ISO 21127:2014 A reference ontology for the
interchange of cultural heritage
information
CIDOC CRM establishes
guidelines for the exchange of
information between cultural
heritage institutions. In simple
terms, this can be defined as
the information managed by
museums, libraries, and
archives.
The intended scope of this
ISO 21127:2014 is defined as
the exchange and integration
of heterogeneous scientific
documentation relating to
museum collections.
CIDOC Conceptual Reference Model (CRM)
International standard: ISO 21127:2014
http://www.cidoc-crm.org/

4. CRM-EH Ontological Model of Archaeological Information Domain - 2003
CRM-EH Ontological
Model initially
modelled the English
Heritage /
Historic England
Archaeological
Information recording
process. But is
applicable to the
more general
archaeological
methodology Single
Context Recording in
the UK (Harris Matrix)

5. CIDOC CRM - CRMarchaeo
“Archaeological Excavation Process” extension – followed on from CRM-EH
Fig. 4: Section drawing with A3 Stratigraphic Interfaces in square brackets [ ], A2 Stratigraphic Volume
Unit in round brackets (), the surfaces S1 and S2 created through A1 Excavation Process Units using
different methodologies and an A7 Embedding of a coin.
A1 Excavation Process Unit
A1 Excavation Process Unit
A3 Stratigraphic Interface
A2 Stratigraphic Volume Unit
A7 Embedding
AP4 produced surface S1
with stratigraphic method
AP4 produced surface S2
with spit excavation method
CRMarchaeo v 1.4.8 (Feb 2019)
Image
Copyright
Lucasfilm

6. Allen Temporal Operators
Relation Inverse
Before (precedes) < After (preceded by) >
Meets m Met by mi
Overlaps o Overlapped by oi
During d Contains di
Starts s Started by si
Finishes f Finished by fi
Equals =
Modeling the Matrix
3 operators that match the
temporality in stratigraphic
relations e.g. Superposition
along with
10 other temporal operators
less explicitly seen in other
archaeological records.
Allen Operators (J.F. Allen 1983):
13 temporal relationships.

7. Modelling the Matrix
“The problem of representing temporal knowledge
and temporal reasoning arises in a wide range of
disciplines including computer science, philosophy,
psychology, and linguistics. In computer science,
it is a core problem of information systems,
program verification, artificial intelligence, and
other areas involving process modeling”
(J.F. Allen 1983, 832)
(RDF: Binding 2011)
STAR project Semantic Query Browser
(Tudhope et al. 2011)
Semantic Technologies for
Archaeological Resources (STAR) 2011
project used stratigraphic relationships
expressed in the excavation matrix
diagrams but often not consistently
formalized in the digital records deposited in
digital archives (ADS).

8. Modelling the Matrix - making explicit all the temporal relationships
Example: Silbury Hill (approx. 2400BC)
Approx. 30m
= 4400 Years
estimated to have involved about
4 million hours of work

9. Would Process Modelling for Analysis activities help?
● Identify common
steps in the
Analysis process
● Identify and clarify
differing
approaches to
process
● Enable semantic
mappings between
common concepts
and terms used in
Analysis
process(es)
Research
Funded
Project
process
Commercial
Developer
Funded
Projects
process
(CRM)
Typical
UK Project
Stages
Published
Stratigraphic
Data
Archived
Stratigraphic
Data
Excavation - Archived
Stratigraphic
Data
Analyzed
Stratigraphic
Data
Re-Use Previous
Excavations
Stratigraphic Data

10. Would Process Modelling for Analysis activities help?
● Identify common steps
in the Analysis process
● Interview
archaeologists in
different organizations
to Identify and clarify
differing approaches to
process
● Enable semantic
mappings between
common concepts and
terms used in Analysis
process(es)
Check Excavation
Stratigraphic Data
Grouping
Stratigraphic Data
Phasing
Stratigraphic Data
Interpreting
Stratigraphic Data
Dating
Stratigraphic Data
Analysis
Specification Diagram of Analysis Grouping & Phasing Processes

11. To Group/Phase/Periodize or not to Group/Phase/Periodize?
Dye&Buck 2.4. Stratigraphic periods and phases
1. The terms “period” and “phase” are defined
variously and sometimes interchangeably by
archaeologists.
2. For the Harris Matrix, a “phase” groups contexts
of similar age, and a “period” groups phases of
similar age, yielding a nested series of time
intervals (Harris, 1989, 158). Defined in this way,
both phases and periods are interpretive
constructs that are typically formulated with
both stratigraphic and non-stratigraphic
information.
3. Because “phase” is also used to describe
Bayesian chronological models, here we use the
term “stratigraphic phase” to refer to a group of
contexts, and the term “chronological phase” to
refer to a time period in a chronological model”.
Units can be grouped into Phases and Periods.
Phases represent structural relations and periods
temporal relations. Units in a phase belong to the
same archaeological structure and units in a period
belong to the same historical epoch. Phases can
also belong to a period
To group units into a Phase select them and chose
Group to Phase from the Edit menu
https://en.wikipedia.org/w/index.php?title=Phase_(archaeology)&oldid=928228844 https://en.wikipedia.org/w/index.php?title=Phase_(archaeology)&oldid=928228844
Harris Matrix Composer – Help file

12. Archaeological sequence diagrams and
Bayesian chronological models - Dye & Buck p87
“Within software such as ‘hm’, it is convenient to
capture the information about dated events in
two tables.
An “event table” associates a directly-dated
archaeological event with its archaeological
context (Fig. 1 illustrated here ->) and indicates
whether the event is directly associated with the
context (KM- “Contemporary”), is older than the
context and thus disjunct (KM- “Residual”), or is
younger than the context and thus disparate (KM-
“Intrusive”) (Dean, 1978).
An “event order table” records information on the
relative ages of archaeological events associated
with the same context (Fig. 1)”
- KM highlights and “Intrusions” 
Dye&Buck Fig. 1. Relational database design for the seven tables of information used to construct
stratigraphic and chronological directed graphs. Note that table names are uppercase, column names
are lowercase, and divided entries define the domain of the column whose name is directly above,
e.g., the unit-type column in the context table contains one of the two values deposit and interface.

13. Bayesian chronological modeling
One difference between a Bayesian chronological model
and an archaeological sequence diagram is that the
Bayesian chronological model may include relationships that
cannot be expressed by simple before/after stratigraphy.
The illustration (Fig. 7) recognizes three (six) possible Allen
temporal relationships between two chronological phases
where one is older than the other. Only two of these
relationships can be represented stratigraphically.
Overlaps in Time relationship
Meets in Time relationship
A Bayesian chronological model comprises directly-dated events and the start and
end dates of one or more chronological phases. The start and end dates of a
chronological phase typically map directly to an archaeological context.
“One chronological phase can be older than the other such that the end date for the
older chronological phase is the same age as the start date for the younger
chronological phase (Fig. 7, middle)”.
Dye & Buck 2015
Fig. 7.
Before/
After
Meets/
Met by
Overlaps/
Overlapped
Allen Temporal Operators

14. Issues with Digital Data in Analysis &
Stratigraphic Standards in Digital Archive contents
❖ Stratigraphy is “the skeleton” of the archaeological site
❖ How do people document Stratigraphic Analysis?
❖ How is an Harris Matrix archived? – just PDF image?
❖ Kept as images or more reusable data?
❖ How readily able to re-use strat relationships?
❖ Need a consistent format for preservation, interchange
sharing and re-use of the Stratigraphic RELATIONSHIPS
❖ E.g. Data as CSV can easily convert to RDF/XML/JSON for
use by semantic technologies
e.g. STELLAR - RDF & Linked Open Data (LOD) outputs
Occurs During
Overlaps
in Time }{
Meets in
Time
Occurs Before/After
Equals
=
e.g. Silbury Hill Matrix

15. Conclusions & Challenges:
FAIR stratigraphic data
including representation of
other Allen relationships
4
● Make this fundamental archaeological data more
sustainably Findable, Accessible, Interoperable and
Reusable (FAIR Principles 2016) across present day
geo-political (period), and spatio-temporal, boundaries?
Recycle FAIRly
Agree standards for sharing digital
stratigraphic data records and enable
better structured Legacy/hardcopy data
3
● Is there a need for an International Convention on
stratigraphic recording, analysis and documentation?
To facilitate better understanding and communication.
Reuse
Data that is fit for purpose
2
● Matrix data should be re-usable effectively e.g. minimum
as CSV files, rather than as images of matrix diagrams buried
in a PDF document.
● Practically derived from existing processes (eg. Harris
Matrix) to facilitate ease of use and re-use
1
• Need more consistent standards in digital records of
stratigraphic and temporal relationships (amongst others)
Reduce
Avoid proliferation of
unnecessary digital materials.
With acknowledgement to Jeremy Huggett (remix is good too!)

16. ● Allen, J.F. (1983) 'Maintaining Knowledge about Temporal Intervals'. Communications of the ACM 26, 11, 832-843.
● Binding, C. (2010) Implementing archaeological time periods using CIDOC CRM and SKOS .The Semantic Web: Research and Applications :
7th Extended Semantic Web Conference, ESWC 2010.
● Cripps, P., Greenhalgh, A. Fellows, D., May, K., David Robinson, D. (2004) Ontological Modelling of the work of the Centre for Archaeology,
CIDOC CRM technical paper: pdf file. Also available: The CRM Diagram, pdf file.
● Dye, T.S. & Buck, C.E. (2015) Archaeological sequence diagrams and Bayesian chronological models.Journal of Archaeological Science, 63.
84 - 93. ISSN 0305-4403
● Harris, E.C. (1979) Principles of Archaeological Stratigraphy (1st Edition). London: Academic Press.
● Huggett, J. Reuse remix recycle: repurposing archaeological digital data. Advances in Archaeological Practice (2018),
doi:10.1017/aap.2018.1
● May, K. 2020 The Matrix: Connecting Time and Space in Archaeological Stratigraphic Records and Archives, Internet
Archaeology 55. https://doi.org/10.11141/ia.55.8
● Papadakis, M., Doerr, M. and Plexousakis, D. "Fuzzy times on space-time volumes," eChallenges e-2014 Conference Proceedings, Belfast,
2014, pp. 1-11.
● Roskams, S. (2001) Excavation. Cambridge: Cambridge University Press.
● Taylor, J.S. (2016) Making Time For Space At Çatalhöyük: GIS as a tool for exploring intra-site spatiotemporality within complex
stratigraphic sequences. PhD thesis, University of York.
● Tudhope, D., May, K., Binding, C. and Vlachidis, A. (2011) 'Connecting Archaeological Data and Grey Literature via Semantic Cross Search',
Internet Archaeology 30. https://doi.org/10.11141/ia.30.5
References & Acknowledgments