CAA2004 " Past the antique - Advanced understanding of the past "

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No general hypothesis of strategies for sequence that identifies with scientific ... is broadened and adjacent in time, possibly complex (my birthday = class of occasions) ...

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April 13-17, 2004 Prato , Italy Supporting Chronological Reasoning in Archeology CAA2004 " Beyond the antique - Digital translation of the past " Martin Doerr Dimitris Plexousakis Katerina Kopaka Chryssoula Bekiari Center for Cultural Informatics Information Systems Laboratory Institute of Computer Science Foundation for Research and Technology Hellas

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Problem Current formal techniques for order are produced for particular cases No general hypothesis of strategies for sequence that identifies with numerical structures of thinking

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Definitions Basic presumptions about occasions in actuality State of undertakings: a particular conveyance of material things, theoretical things and occasions over space-time. every occasion is broadened and touching in time, conceivably complex ( my birthday = class of occasions ) there are no insignificant components of occasions, no restrictions to disintegration or piece (scale-free hypothesis) The genuine start and end of an occasion are not recognizable, but rather for a date it might be decidable on the off chance that it is some time recently, after or inside an occasion.

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Historical occasions as gatherings… t Brutus lucidness volume of Caesar's passing Caesar's mom Brutus' blade rationality volume of Caesar's introduction to the world S

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Deposition occasion as gatherings… t magma and remnants antiquated Santorinian intelligibility volume of spring of gushing lava ejection house spring of gushing lava cognizance volume of house building S Santorini - Akrotiti

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Information trade as gatherings… t soundness volume of second declaration intelligence volume of first declaration 2 nd Athenian 1 st Athenian different Soldiers runner intelligibility volume of the clash of Marathon S Marathon Athens

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P81 continuous all through E61 Time Primitive P82 sooner or later inside E61 Time Primitive P83 had in any event length E54 Dimension P84 had at most term E54 Dimension Time-traverse Information P86 falls with in (contains) P114 – P120 is equivalent time to completions is done by begins is begun by happens amid incorporates … E52 Time-Span P4 has time-traverse ( is time-traverse of ) E2 Temporal Entity P9 comprises of (structures some portion of) E4 Period P12 happened within the sight of (was available at) E77 Persistent Item E5 Event P92 brought into presence (was brought into presence by E21 Person P93 removed from presence (was removed from presence by E18 Physical stuff E64 End of Existence E63 Begin of Existence

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Definitions Goal of Chronology All dating is about occasions (question : more often than not = generation and so on occasion) assurance of insignificant indeterminacy time-interims for an occasion or for start and end of an occasion/period. assurance of the likelihood of an occasion to have happened at certain time Process of Chronology assurance of all order applicable conceivable conditions of issues steady with given proof assurance of the most plausible situation reliable with given confirmation

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Events and Time ETS = ( E, TM, h, π ) , where E is a denumerable arrangement of discrete occasions or periods TM is a direct time demonstrate characterized as the 6-tuple TM = (D, T, u, l,  ), where: D is the arrangement of Julian dates d viewed as genuine numbers (i.e. given in years, milliseconds or any granularity of time). T  (D X D) is an arrangement of curved time interims indicated by their endpoints. u(t), t  T is a capacity mapping the more noteworthy (upper) interim endpoint to a component of D. l(t), t  T is a capacity mapping the littler (lower) interim endpoint to a component of D.  is the entire worldly request on D h is a capacity mapping each component e  E to a component t  T , which speaks to the genuine time interim all through which the occasion or period is occurring . π is a capacity mapping each component e  E and d  D to a likelihood dispersion work f that profits the likelihood of an occasion or period to happen ("on-going") at time d . Occasion/Time structure (ETS)

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Events and Time genuine start l(h(e)) genuine end u(h(e)) determinacy interim( D2 ) indeterminacy interim ( D1 ) before the occasion after the occasion Event "occasion power " Indeterminacy of start( D3 ) Indeterminacy of end( D4 ) time in the occasion

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Determination connections Determination connections of an interim t  T with an occasion e: (D1) Indeterminacy: i(t,e)  h(e)  t . (D2) Determinacy: d(t,e)  h(e)  t. (D3) Indeterminacy of start: b(t,e)  l(h(e))  t. (D4) Indeterminacy of end: e(t,e)  u(h(e))  t. A few connections between two time interims t 1, t 2  T (R1) t 1  t 2   d 1  t 1 : d 1  l(t 2 ) (genuinely before) (R2) t 1  t 2   d 1  t 1 : d 1  u(t 2 ) (not after, "until the end") (R3) t 1  t 2   d 1  t 1 : d 1  l(t 2 ) (not some time recently, "from the beginning") An expansion of a period interim t with an interim li of worldly term values l (S1) t + li =  d  D:  d1  t, l  li  d=d1+l 

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Elements of sequential thinking Absolute sequence Matching with novel transient example ( dendrochronology ) Historical record of real perception in respect to a schedule ( Maya timetable, astronomic occasions ..) or intermittent occasions ( Olympic amusements, seasons… … ) By condition of fleeting procedure with known impact on a question ("maturing") ( C14, potassium-argon, uranium arrangement … ..) => indeterminacy interims indeterminacy interims obliging the genuine time of the occasion ( D1-D4 ), perhaps refined by likelihood dispersion inside this interim various datings => crossing point of interims/joining probabilities yielding refined interims/probabilities

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Elements of ordered thinking Relative sequence by occasion arrange from "causal" connections between occasions, i.e. fundamental essentials of an occasion to happen. support in a meeting must be at/after creation and at/before obliteration of all members ( individuals and things, for example, strata, objects, instruments, structures, vehicles and so forth .) exchange of data by means of meeting chains of data bearers (individuals, objects) at/after making of data and before loss of last transporter(?) . ( e.g. the runner from Marathon achieving Athens ) chronicled record of genuine perceptions ( lords records, chain of commands and so forth .) Order of follows ( icy mass scratches, testimony arrangement, building grouping cellar to-rooftop ) => fleeting systems obliging indeterminacy interims ( h(e i )  h(e j ), h(e i )  h(e j ), h(e i )  h(e j ). . ) with variable dates. joined with components of outright sequence, potentially reached out by probabilistic hypothesis yielding refined interims/probabilities

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Elements of dating Relative order by consideration - A bigger, on-going procedure contains sub-forms that can be dated independently (moderately or completely) statement of one protest in a grid a solitary murdering/decimation in a fight/war taking confirmation from: "causal" connections i.e. important constituent of an occasion to happen. chronicled records of real perceptions Inclusion of follows (affidavit consideration, incorporation in assembled structure, skull on a combat zone, and so on ) => dating of every sub occasion gives an imperative to the bigger occasion to be on-going, for example, h(e i )  h(e l ) (disparities amongst inward and external limits.)

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Elements of dating Relative sequence by transient separations and terms from: foundation learning of greatest/normal lifetime (human life, normal utilize time of an earth pot and so on.) additionally: intermittent separations, for example, commemorations, feasts, peaceful regular developments, country schedules verifiable record of genuine perceptions relating the span of an impact to an estimation of rate of progress testimony profundity and statement rate change of style/innovative aptitudes and style change rate tooth scraped area, bones age sign, skeleton stays spatial separation and correspondence trade (voyaging speed) => imbalances contain aggregates of variable dates and given fleeting separations, for example, h(e i )+li  h(e j ) .

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Elements of dating " Categorical/Typological dating " the creation occasions ( p(o i )) of one write C of things ( o i ) (antiquities – ecofacts) fall inside a known spatiotemporal degree P(C) := inf  t  T :  o i  C  h(p(o i ))  t  characterization joined with (likelihood) appropriation of generation occasions consolidates instability of grouping with vulnerability of creation circulation. after arrangement remains an incorporation issue estimation of the fleeting request of the appearances of sorts = the generation occasions of one kind of things are after the creation occasions of another kind of things exemplary and antiquated style and so on (additionally yet legacies) => grouping and disparities amongst internal and external limits

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Conclusions We characterize conditions of issues with respect to their part in numerical speculations as components for sequential thinking : Absolute sequence Relative order by occasion arrange Relative order by consideration Relative sequence by worldly separations and spans Categorical/Typological dating This is a preparatory study proposed to bolster a more summed up hypothesis of sequential thinking in archaic exploration and history.