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CAA2004 “Beyond the artifact Digital interpretation of the past”
April 13-17, 2004
Prato, Italy
Supporting Chronological Reasoning in
Archaeology
Martin Doerr
Dimitris Plexousakis
Katerina Kopaka
Chryssoula Bekiari
Centre for Cultural Informatics
Information Systems Laboratory
Institute of Computer Science
Foundation for Research and Technology Hellas
Problem

Current formal methods for chronology are developed
for specific cases

No overall theory of methods for chronology that
relates to mathematical frameworks of reasoning
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Definitions

Basic assumptions about events in reality
– State of affairs: a specific distribution of material
items, conceptual items and events over spacetime.
– each event is extended and contiguous in time,
potentially complex (my birthday = class of events)
– there are no minimal elements of events, no limits
to decomposition or composition (scaleindependent theory)
– The true begin and end of an event are not
observable, but for a date it may be decidable if it
is before, after or within an event.
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Historical events as meetings…
t
Brutus
Caesar’s
mother
coherence
volume of
Caesar’s death
Caesar
Brutus’
dagger
coherence
volume of
Caesar’s birth
S
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Deposition event as meetings…
t
lava and
ruins
ancient
Santorinian
coherence volume
of volcano eruption
house
volcano
coherence
volume of
house building
Santorini - Akrotiti
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S
5
Information exchange as meetings…
t
coherence volume of
second announcement
coherence volume of
first announcement
other
Soldiers
2nd Athenian
1st Athenian
runner
coherence volume
of the battle of
Marathon
Marathon
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Athens
S
6
Time-span Information
P114 – P120
is equal time to
finishes
is finished by
starts
is started by
occurs during
includes
………
P81 ongoing
throughout
E61 Time Primitive
E52 Time-Span
P82 at some
time within
E61 Time Primitive
P4 has time-span
(is time-span of)
P83 had at
least duration
E54 Dimension
P84 had at
most duration
E54 Dimension
P86 falls with in
(contains)
E2 Temporal Entity
P9 consists of
(forms part of)
E4 Period
E77 Persistent Item
E5 Event
E21 Person
E18 Physical stuff
E63 Begin of Existence
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E64 End of Existence
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Definitions

Goal of Chronology
– All dating is about events (object : usually = production etc.
event)
– determination of minimal indeterminacy time-intervals for an
event or for begin and end of an event / period.
– determination of the probability of an event to have
happened at certain time

Process of Chronology
– determination of all chronology-relevant possible states of
affairs consistent with given evidence
– determination of the most probable state of affairs
consistent with given evidence
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Events and Time
ETS
TM, h,
π ), where
Event=/( E,
Time
structure
(ETS)
E is a denumerable set of discrete events or periods
TM is a linear time model defined as the 6-tuple TM = (D, T, u, l,  ),where:
D is the set of Julian dates d regarded as real numbers
(i.e. given in years, milliseconds or any granularity of time).
 T (D X D) is a set of convex time intervals specified by their endpoints.
 u(t), tT is a function mapping the greater (upper) interval endpoint to an
element of D.
 l(t), tT is a function mapping the smaller (lower) interval endpoint to an
element of D.
  is the complete temporal order on D
h
is a function mapping every element e E to an element tT, which represents the true time interval
throughout which the event or period is happening.
π is a function mapping every element e E and dD to a probability distribution function f
that returns the probability of an event or period to be happening (“on-going”) at time d.
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Events and Time
true begin
l(h(e))
true end
u(h(e))
“event intensity”
indeterminacy interval (D1)
before the event
after the event
Indeterminacy
of begin(D3)
Indeterminacy
of end(D4)
time
in the event
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Determination relationships
Determination relationships of an interval t  T with an
event e:
(D1) Indeterminacy: i(t,e)  h(e)  t.
(D2) Determinacy: d(t,e)  h(e)  t.
(D3) Indeterminacy of begin: b(t,e)  l(h(e))  t.
(D4) Indeterminacy of end: e(t,e)  u(h(e))  t.
Some relationships between two time intervals t1, t2 
T
(R1) t1  t2   d1 t1: d1 l(t2) (truly before)
(R2) t1  t2   d1 t1: d1 u(t2) (not after, “until the end”)
(R3) t1  t2   d1 t1: d1 l(t2) (not before, “from the
beginning”)
An addition of a time interval t with an interval li of temporal duration
values l
(S1) t + li =  d  D:  d1  t, l  li  d=d1+l 
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Elements of chronological reasoning

Absolute chronology
– Matching with unique temporal pattern (dendrochronology)
– Historical record of actual observation relative to a calendar (Maya
calendar, astronomic events..) or periodic events (Olympic games,
seasons……)
– By state of temporal process with known effect on an object
(“aging”) (C14, potassium-argon, uranium series…..)

=> indeterminacy intervals
– indeterminacy intervals constraining the true time of the event
(D1-D4), possibly refined by probability distribution within this
interval
– multiple datings => intersection of intervals / combining
probabilities yielding refined intervals / probabilities
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Elements of chronological reasoning

Relative chronology by event order from
– “causal” relationships between events, i.e. necessary prerequisites of
an event to happen.
– participation in a meeting must be at/after creation and at/before destruction of
all participants (people and things such as strata, objects, tools, buildings, vehicles etc.)
– transfer of information via meeting chains of information carriers (people,
objects) at/after creation of information and before loss of last carrier(?). (e.g. the
runner from Marathon reaching Athens)
– historical record of actual observations (kings lists, totem poles etc.)
– Order of traces (glacier scratches, deposition sequence, building sequence basementto-roof)

=> temporal networks
– constraining indeterminacy intervals (h(ei)  h(ej), h(ei)  h(ej), h(ei)  h(ej)..) with
variable dates.
– combined with elements of absolute chronology, possibly extended by
probabilistic theory yielding refined intervals / probabilities
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Elements of dating

Relative chronology by inclusion A larger, on-going process contains sub-processes that can be dated individually
(relatively or absolutely)
– deposition of one object in a matrix
– a single killing/ destruction in a battle/war
taking evidence from:
– “causal” relationships i.e. necessary constituent of an event to
happen.
– historical records of actual observations
– Inclusion of traces (deposition inclusion, inclusion in built structure,
skull on a battle field, etc. )

=> dating of each sub event provides a constraint for the larger
event to be on-going: such as h(ei)  h(el) (inequalities between
inner and outer bounds.)
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Elements of dating

Relative chronology by temporal distances and durations from:
– background knowledge of maximum / average lifetime
(human life, average use period of a clay pot etc.)
–
also: periodic distances such as anniversaries, feasts, pastoral seasonal
movements, rural calendars
– historical record of actual observations
– relating the size of an effect to an estimation of rate of
change
–
–
–
–

deposition depth and deposition rate
change of style/ technological skills and style change rate
tooth abrasion, bones age indication, skeleton remains
spatial distance and communication exchange (traveling speed)
=> inequalities contain sums of variable dates and given
temporal distances such as h(ei)+li  h(ej).
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Elements of dating

“Categorical / Typological dating”
– the production events (p(oi)) of one type C of things (oi)
(artifacts – ecofacts) fall within a known spatiotemporal
extent P(C) := inf t T :  oi C  h(p(oi))  t 
– classification combined with (probability) distribution of production
events
– combines uncertainty of classification with uncertainty of production
distribution.
– after classification remains an inclusion problem
– estimation of the temporal order of the appearances of
types = the production events of one type of things are after
the production events of another type of things
– classic and archaic style etc. (also but heirlooms)

=> classification and inequalities between inner and outer
bounds
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Conclusions

We classify states of affairs regarding their role in
mathematical theories as elements for chronological
reasoning :
– Absolute chronology
– Relative chronology by event order
– Relative chronology by inclusion
– Relative chronology by temporal distances and durations
– Categorical / Typological dating

This is a preliminary study intended to support a
more generalized theory of chronological reasoning
in archeology and history.
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