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

1. April 13-17, 2004 Prato, Italy Supporting Chronological Reasoning in Archaeology CAA2004 “Beyond the artifact - Digital interpretation of the past” 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

2. 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

3. 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.

4. 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

5. Deposition event as meetings… t lava and ruins ancient Santorinian coherence volume of volcano eruption house volcano coherence volume of house building S Santorini - Akrotiti

6. 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

7. P81ongoing throughout 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

8. 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

9. 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), tT isa function mapping the greater (upper) interval endpoint to an element of D. • l(t), tT 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 tT, which represents the true time interval throughout whichthe event or period is happening. • πis 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. Event / Time structure (ETS)

10. Events and Time 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

11. 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 

12. 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

13. 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

14. 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.)

15. 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).

16. 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

17. 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.