The representation of logical cycle processes in views

Cycle processes (loops) are an interesting logical phenomenon. Cycle processes are indispensable for the description of real phenomena. Below, we are going to demonstrate how such cycle processes (loops) can be represented with the logodynamic tools of LDC.

What is a logical cycle process (loop)?

A loop is a well-known practical programming problem:
 
IF (A) THEN (B) AND

IF (B) THEN (A)

When these two logic instructions occur in a computer program or another algorithm, the program will “loop”. As soon as A has been executed, B will also have to be executed, and when B has been executed, A will have to be executed again, and then B again. The two instructions trigger each other off – ad infinitum.

 A → B → A → B → A → B

The consequence is that – unless the loop situation is actively prevented or interrupted – the program will execute these two steps endlessly. From the outside, this will look as if the program is standing still; it has “suspended” itself.

Real loops 

The same type of loop does not solely occur in mathematics and computer programs, however, but also in real life, i.e. in real people’s thoughts and actions – in other words, with all of us.

If the consequences of such loops are negative for us, we speak of a vicious circle. Yet loops need not only have negative effects; in real life, there are situations where A and B reinforce each other in a perfectly positive manner, so we speak of a virtuous circle.

Loops in logic systems

Conventional logic systems, including FOL (First Order Logic) are incapable of representing such real loops, classical logic being too rigid for this at its core. This cannot be changed. Nor can extensions of logic in terms of modal logic or fuzzy logic prevent the problem of loops. Dynamic logic (logodynamics), however, is able to describe real loop situations with both simplicity and precision.

 Properties of a logical cycle (loop)

1. Closedness

Logical cycles are closed logical circuits whose elements reinforce each other (closed circuit of reinforcement relationships).

View 1: A typical loop

2. Stability = the survival of a system over time

Mutual reinforcement provides such cycles with a high degree of stability. This entails that they survive for a certain duration in time. Everything that exists in reality has to survive in time; otherwise, it does not really exist.

My proposition is that a closed logical cycle is a requirement in every existing entity.
 

Are loops always stable?

Although loops tend to stop time, as it were, they never exist forever in reality. Nothing exists eternally. In reality, the forces involved in a loop are always part of a context of further forces which dissolve the loop at some stage in the future.

Loops, whether they be virtuous or vicious circles, dissolve in two ways:

• Escalation
   - There is a showdown which changes the situation definitively (such as the defeat of Hitler’s Germany in 1945).
• De-escalation
   The forces involved – such as players A and B in View 1 – change their strategies
   - through realising their own defeat,
   - through realising the negative consequences of further escalation,
   - through external forces.

The cycle can be dissolved by means of escalation or de-escalation:

View 2: Escalation and de-escalation guide the players out of the loop

Escalation will cause the forces involved to become exhausted, for keeping the cycle process going requires a constant supply of resources, which in the case of an escalation will soon reach its limits.

Although the cycle process with its consistent reinforcement relations appears to be stable, the finite nature of resources will ultimately end the escalation. Limitless growth is not possible in any loop situation, either.
 

The end of stability

Ultimately, every loop will be interrupted by an escalation, which may look as follows:

View 3: Escalation of the loop and possible consequences

In the view drawn above, two scenarios are indicated: the escalation may lead to A’s or B’s destruction owing to their lack of resources, for example. Additionally, there is still a possibility of finding a way towards de-escalation in spite of the advanced nature of the conflict. In both cases, the seemingly inevitable vicious circle is broken.

The emergence of a loop

If two parties are involved in a vicious circle, there are at least two views of what is happening: that of A and that of B.

Country A feels threatened by country B and therefore arms itself.
Country B feels threatened by A’s armament and therefore has a reason for arming itself in turn.

View 4: A’s view (Opinion A)

B’s view is reciprocal:         

View 5: B’s view (Opinion B)

In reality, the views (opinions) of A and B meet and constitute a loop:

View 6: The fully developed loop

Or, put in simpler terms:

View 7: Simple representation of the loop

Who started it? – Although both A and B will emphasise that the opposite side started it all, the start is irrelevant to the continued existence of the loop. Once it has gained momentum, it will continue automatically, and it is often impossible for outsiders to discover where it all started.

Vicious circle or virtuous circle?

No matter whether a circle is vicious or virtuous – both are loops, but one with a positive effect and the other with a negative effect. What is identical in both cases is the self-reinforcement of the process once it has started. LDC represents the progression of the forces with reinforcement arrows (→) without making a good/evil valuation.

After all, the valuation is not IN the loop, but AROUND the loop. What impact does the loop have on the outside? Precisely this can also be represented in LDC, in that relations from individual stations (arguments) of the loop lead towards the outside or in that the entire loop reacts as an entity with the outside. For this purpose, the loop is placed into a subview in the view, which represents the entity.

Result: an open system

A loop as represented in view 6 or 7 looks inescapable. If the relationship arrows of these views had the same significance as the IF-THEN relationship of classic logic, the cycle process could not be stopped in all eternity.

In reality, however, this is not the case. This is why the classic mathematical, i.e. static, logic is unsuitable for the complete representation of real processes.

Dynamic logic refrains from regarding the IF-THEN relationship as absolute. No conclusion is absolutely imperative. No matter how obvious a consequence may look, it may fail to occur in some cases.

This has something to do with the fact that the picture (the view) is never complete. Further forces (arguments) may have an impact from the outside at any time. The issues that really interest us are always issues of an open system.