User:Fieryjaguar1/sandbox/Faulkner-Bennett diagram

A Faulkner-Bennett diagram (also known as a Plan diagram) is a diagram that shows any plan or series of events between the current state and a future state or states. Adjacent lines show alternate plans which can be connected to the main one, and points on these and the main line show events, choices, or changes in circumstance. The actual course of events taken can be listed using a special notation. These diagrams were conceived in 2015 by logicians Gavin Faulkner and Alexander Bennett for the purpose of explaining series of events and logical contingencies. It is a type of flowchart.

Example


This image shows a basic Faulkner-Bennett diagram. It contains two phases and the usual baseline, starting at $$\alpha$$ and ending at $$\omega_{1}$$. There are many subplans or contingencies, which are connected to each other in various ways. All junctions are marked.

Structure
Faulkner-Bennett diagrams follow a clear and concise structure, divided into plans, phases, and points.

Baseline


The baseline of a Faulkner-Bennett diagram is the basic plan outline. It begins at $$\alpha$$, which represents the starting position before the plan is enacted, and ends at $$\omega_{1}$$, which is the ideal final position after the plan concludes.

Phases


Each diagram is divided into phases. There can be any number of these, and they are divided using vertical lines on the baseline up. They are numbered using Roman numerals in ascending order as the distance increases from $$\alpha$$. In the diagram above, there are two phases, I and II. It is common to see higher numbers of phases as the total length of the plan increases. Higher-numbered phases are done so to indicate increasing levels of unpredictability.

Points


Key to the concept of the Faulkner-Bennett diagram is that of points. Points can be on the baseline or any other plan line, and represent a variety of things. In the above diagram, there are four points: $$\alpha$$, the starting point, $$\omega_{1}$$, the ending point, $$a$$ and $$b$$, two event points.

Points come in different varieties depending on what, if anything, changes at their occurrence. The three main types of points are:

Naming
While each point is often referred to by a relative name to its line (i.e., the first point on a line is $$a$$, the second is $$b$$, and so on), it can also be referred to by an absolute name, such that each individual point in a single diagram has a unique name.

For instance, the first point on the baseline after $$\alpha$$ is often labelled just $$a$$, but has an absolute name of: $$a_{1}$$. The second point on a contingency extending from an external junction $$e$$ in phase III has a relative name of $$b$$, but an absolute name of $$e_{3}(b)$$. The third point on a second-level contingency in phase III extending from an internal junction $$f$$ in phase II extending from an external junction $$a$$ in phase I could be $$c$$ or $$a_{1}[f'_{2}(c)]$$

Alternates


Whenever the plan reaches a junction point, like $$a$$ in the diagram, there is a possibility of continuing on the baseline, but also the possibility of going to another plan line, known as an alternate or contingency. The points on the contingency reset back to $$a$$. Contingencies can both stack and return to the baseline, like at $$b$$ in the diagram.

The formula for staying on this baseline is: $$\alpha, a, b, \omega_{1}$$

The formula for entering on the contingency at $$a$$ is: $$\alpha, a\uparrow(a, b), \omega_{1}$$

Notation
There is a notation for writing out specific paths on a given diagram. The example used in this article has a large, though finite, number of possible paths. The simplest path is always that of the baseline. The baseline path of the given diagram is given thus:

$$ \alpha, a, b, c, d, e, f, 2a, \omega_{1} $$

where each Arabic numeral indicates a change in phase, each comma indicates the start of a new point, $$\alpha$$ indicates the starting point, $$\omega_{x}$$ represents an ending variant $$x$$, and each series of lowercase Roman letters is a point.

Another, more complicated, path of the diagram is thus:

$$\alpha, a\Uparrow \Bigg[a, b\Uparrow \Bigg(a, b\downarrow \bigg(a, b^{1}\Uparrow \Big(a, b\rightarrow 2c\uparrow \big(a \big)\Big)\bigg)\Bigg)\Bigg], \omega_{4}$$

where previous definitions apply, $$\uparrow$$ represents a shift to a contingency away from the current plan and baseline, $$\downarrow$$ is a shift to a contingency closer to the baseline, $$\rightarrow$$ represents a contingency that crosses phase lines, and $$\{ [(x)] \}$$ represents ascending plans away from the baseline. ''Note: the $$a, b, c, ... $$ notation for points resets to $$a$$ at every phase change and every plan change.''

An explanation of all used conventions: