Chris little allen diagram

23-049/sections/06-abstract_model.adoc

@@ -121,10 +121,12 @@ In this regime, no clocks or time measurements are defined, only events, that ar
 
 One set of events may be completely ordered with respect to each other, but another set of similar internally consistent ordered events cannot be cross-referenced to each other unless extra information is available. Even then, only partial orderings may be possible.
 
-In this regime, the <<temporal_knowledge,Allen Operators>> can be used. If A occurs before B and B occurs before C, then that A occurs before C can be correctly deduced. The full set of operators also covers pairs of intervals. So in our example, B occurs in the interval (A,C). However, arithmetic operations like (B-A) or (C-A) cannot be performed as any timescale or measurements are not defined. For example, in geology, 'subtracting' Ordovician from Jurassic is meaningless. In archeology, 'subtracting' a layer with a certain type of pottery remains from the layer containing burnt wood and bones is again not meaningful. Only the ordering can be deduced.
+In this regime, the <<temporal_knowledge,Allen Operators>> (see Figure 2) can be used. If A occurs before B and B occurs before C, then that A occurs before C can be correctly deduced. The full set of operators also covers pairs of intervals. So in our example, B occurs in the interval (A,C). However, arithmetic operations like (B-A) or (C-A) cannot be performed as any timescale or measurements are not defined. For example, in geology, 'subtracting' Ordovician from Jurassic is meaningless. In archeology, 'subtracting' a layer with a certain type of pottery remains from the layer containing burnt wood and bones is again not meaningful. Only the ordering can be deduced.
 
 This regime constitutes an Ordinal Temporal Reference System, with discrete enumerated ordered events.
 
+image::images/IntervalRelations.jpg[align="center"]
+
 === Simple Clocks and Discrete Timescales
 
 In this regime, a clock is defined as any regularly repeating physical phenomena, such as pendulum swings, earth's rotation about the sun, earth's rotation about its axis, heart beats, vibrations of electrically stimulated quartz crystals or the resonance of the unperturbed ground-state hyperfine transition frequency of the cesium-133 atom. In terms of the number of repetitions possible, some phenomena make better clocks than others, because of the consistency of each repetition and the precision of each 'tick'. A mechanism for counting, or possibly measuring, the ticks is desirable.
@@ -139,7 +141,7 @@ It may seem that time can be measured between 'ticks' by interpolation, but this
 
 The internationally agreed atomic time, TAI, is an example of a timescale with an integer count as the measure of time. However in practice, TAI is an arithmetic compromise across about two hundred separate atomic clocks, corrected for differing altitudes and temperatures.
 
-In this regime, <<temporal_knowledge,Allen Operators>> also can be used. If L occurs before M and M occurs before N, that L occurs before N can be correctly deduced. The full set of operators also covers pairs of intervals. So if M occurs in the interval (L,N),  integer arithmetic operations such as (M-L) or (N-L) can be performed. This is because an integer timescale or measurement is defined.
+In this regime, <<temporal_knowledge,Allen Operators>> (see Figure 2) also can be used. If L occurs before M and M occurs before N, that L occurs before N can be correctly deduced. The full set of operators also covers pairs of intervals. So if M occurs in the interval (L,N),  integer arithmetic operations such as (M-L) or (N-L) can be performed. This is because an integer timescale or measurement is defined.
 
 This regime constitutes a Temporal Coordinate Reference System, with discrete integer units of measure which can be subject to integer arithmetic.
 
@@ -153,7 +155,7 @@ It is also assumed that time can be extrapolated to before the time when the clo
 
 This gives us a continuous number line to perform theoretical measurements. This is a coordinate system. With a datum/origin/epoch, a unit of measure (a name for the 'tick marks' on the axis), positive and negative directions and the full range of normal arithmetic. This is a Coordinate Reference System (CRS).
 
-In this regime, the <<temporal-knowledge,Allen Operators>> also can be used. If A occurs before B and B occurs before C, that A occurs before C can be correctly deduced. The full set of operators also covers pairs of intervals. So if B occurs in the interval (A,C), real number arithmetic operations like (B-A) or (C-A) can be performed. This is because a timescale or measurement has been defined, and between any two instants, an infinite number of other instants can be found.
+In this regime, the <<temporal-knowledge,Allen Operators>> (see Figure 2) also can be used. If A occurs before B and B occurs before C, that A occurs before C can be correctly deduced. The full set of operators also covers pairs of intervals. So if B occurs in the interval (A,C), real number arithmetic operations like (B-A) or (C-A) can be performed. This is because a timescale or measurement has been defined, and between any two instants, an infinite number of other instants can be found.
 
 [example]
 Some examples are:
@@ -167,7 +169,7 @@ This regime constitutes a Temporal Coordinate Reference System, with a continuou
 
 In this regime, counts and measures of time are related to the various combinations of the rotations of the earth, moon and sun or other astronomical bodies. There is no simple arithmetic. For example, the current civil year count of years in the Current Era (CE) and Before Current Era (BCE) is a very simple calendar, as there is no year zero. That is, Year 14CE – Year 12CE is a duration of 2 years, and Year 12BCE - Year 14BCE is also two years. However Year 1CE - Year 1BCE is one year, not two as there is no year 0CE or 0BCE.
 
-In this regime, the use of the <<temporal_knowledge,Allen Operators>> is not straightforward. If A occurs before B and B occurs before C, then correctly deducing that A occurs before C is not always easy. The full set of Allen Operators also covers pairs of intervals. So in the example, B occurs in the interval (A,C). However, simple arithmetic operations like (B-A) or (C-A) cannot usually be done simply because of the vagaries of the calendar algorithms, multiple timescales, and multiple Units of Measure.
+In this regime, the use of the <<temporal_knowledge,Allen Operators>> (see Figure 2) is not straightforward. If A occurs before B and B occurs before C, then correctly deducing that A occurs before C is not always easy. The full set of Allen Operators also covers pairs of intervals. So in the example, B occurs in the interval (A,C). However, simple arithmetic operations like (B-A) or (C-A) cannot usually be done simply because of the vagaries of the calendar algorithms, multiple timescales, and multiple Units of Measure.
 
 Calendars are social constructs made by combining several clocks and their associated timescales.
 
@@ -428,5 +430,4 @@ The geospatial community has often used analogies between space and time to cons
 
 These are not symmetrical in space and time.
 
-Temporal constructs such as instants, durations or intervals, multi-instants (a set of instants), and multi-intervals are not included in this conceptual model. These do have strongly analogous equivalents in space, such as points and multi-points, especially in a single dimension, such as vertical. The temporal constructs are well described in <<temporal_knowledge,Maintaining Knowledge about Temporal Intervals by J. F. Allen>> and apply across all of the regimes, so do not need to be in this Abstract Conceptual Model.
-
+Temporal constructs such as instants, durations or intervals, multi-instants (a set of instants), and multi-intervals are not included in this conceptual model. These do have strongly analogous equivalents in space, such as points and multi-points, especially in a single dimension, such as vertical. The temporal constructs are well described in <<temporal_knowledge,Maintaining Knowledge about Temporal Intervals by J. F. Allen>> (see Figure 2) and apply across all of the regimes, so do not need to be in this Abstract Conceptual Model.