temporal reasoning CAA 04 12

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Information about temporal reasoning CAA 04 12
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Published on May 2, 2008

Author: Penelope

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CAA2004 “Beyond the artifact - Digital interpretation of the past” :  CAA2004 “Beyond the artifact - Digital interpretation of the past” Centre for Cultural Informatics Information Systems Laboratory Institute of Computer Science Foundation for Research and Technology Hellas April 13-17, 2004 Prato, Italy Supporting Chronological Reasoning in Archaeology Martin Doerr Dimitris Plexousakis Katerina Kopaka Chryssoula Bekiari Problem:  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:  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. Slide4:  S t Caesar’s mother Caesar Brutus Brutus’ dagger coherence volume of Caesar’s death coherence volume of Caesar’s birth Historical events as meetings… Slide5:  S t ancient Santorinian house lava and ruins volcano coherence volume of volcano eruption coherence volume of house building Santorini - Akrotiti Deposition event as meetings… Slide6:  S t runner 1st Athenian coherence volume of first announcement coherence volume of the battle of Marathon Marathon other Soldiers Athens 2nd Athenian coherence volume of second announcement Information exchange as meetings… Slide7:  E21 Person E52 Time-Span P4 has time-span (is time-span of) E64 End of Existence E4 Period E63 Begin of Existence E5 Event P9 consists of (forms part of) P12 occurred in the presence of (was present at) P86 falls with in (contains) Time-span Information P114 – P120 is equal time to finishes is finished by starts is started by occurs during includes ……… E2 Temporal Entity E77 Persistent Item E18 Physical stuff P92 brought into existence (was brought into existence by P93 took out of existence (was taken out of existence by Definitions:  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:  Events and Time Event / Time structure (ETS) ETS = ( E, TM, h, π ), where 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. Slide10:  time after the event in the event before the event “event intensity” true begin l(h(e)) true end u(h(e)) indeterminacy interval (D1) determinacy interval(D2) Indeterminacy of begin(D3) Indeterminacy of end(D4) Events and Time Determination relationships:  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:  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 Slide13:  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 chronological reasoning Elements of dating:  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:  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:  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:  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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