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CAA2004 “ Beyond the artifact - Digital interpretation of the past ”

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### CAA2004 “Beyond the artifact - Digital interpretation of the past”

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

Definitions

- Basic assumptions about events in reality
- State of affairs: a specific distribution of material items, conceptual items and events over space-time.
- 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 (scale-independent 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.

Historical events as meetings…

t

Brutus

coherence volume of Caesar’s death

Caesar

Caesar’s mother

Brutus’ dagger

coherence volume of Caesar’s birth

S

t

lava and

ruins

ancient

Santorinian

coherence volume of volcano eruption

house

volcano

coherence volume of house building

S

Santorini - Akrotiti

Information exchange as meetings…

t

coherence volume of second announcement

coherence volume of first announcement

2nd Athenian

1st Athenian

other

Soldiers

runner

coherence volume of the battle of Marathon

S

Marathon

Athens

E61 Time Primitive

P82at some time within

E61 Time Primitive

P83 had at least duration

E54 Dimension

P84 had at most duration

E54 Dimension

Time-span Information

P86falls with in

(contains)

P114 – P120

is equal time to

finishes

is finished by

starts

is started by

occurs during

includes

………

E52 Time-Span

P4has time-span

(is time-spanof)

E2 Temporal Entity

P9 consists of

(forms part of)

E4 Period

P12occurred in the presence of

(was present at)

E77 Persistent Item

E5 Event

P92 brought into existence

(was brought into existence by

E21 Person

P93 took out of existence

(was taken out of existence by

E18 Physical stuff

E64 End of Existence

E63 Begin of Existence

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

Events and Time

- ETS = ( E, TM, h, π ), where
- Eis a denumerable set of discrete events or periods
- TMis a linear time model defined as the 6-tuple TM = (D, T, u, l, ),where:
- Dis 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), tT isa function mapping the greater (upper) interval endpoint to an element of D.
- l(t), tT isa function mapping the smaller (lower) interval endpoint to an element of D.
- is the complete temporal order on D
- hisa function mapping every element e E to an element tT, which represents the true time interval throughout whichthe event or period is happening.
- πis a function mapping every element e E and dD to a probability distribution function f
- that returns the probability of an event or period to be happening (“on-going”) at time d.

Event / Time structure (ETS)

true begin

l(h(e))

true end

u(h(e))

determinacy

interval(D2)

indeterminacy interval (D1)

before the event

after the event

Event

“eventintensity”

Indeterminacy

of begin(D3)

Indeterminacy

of end(D4)

time

in the event

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

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 anobject(“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

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 basement-to-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

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.)

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).

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

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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