Beginning to relate Multiple Form Logic with «PILE objects»…

This first attempt to investigate (possible) relationships between «Pile» and «Multiple Form Logic» is based on Ralph Westphal‘s paper «Freeing Data From the Silos: A Relationistic Approach to Information Processing» (pdf). Ralph’s abstract is the following:

Abstract
Current data processing is limited by a container-reference dichotomy. Data once stored and connected is hard to rearrange and connect in new ways equired by needs that have changed over time. This paper explains an approach to remove this fundamental limitation. It argues data should no longer be recorded and stored, but assimilated and represented/described. Instead of copying data into data structure for further processing, data should be described by a “system of pure relations” in which the data itself is nowhere to be found anymore, but can be regenerated as needed. The benefits of such a “system of pure relations” are infinite connectability of data at any level of abstraction.

Here is an important part of Ralph Westphal’s paper, which is relevant to Multiple Form Logic (page 10):

Pile: A System of Pure Relations.
To overcome the container-reference dichotomy current data models have to be abandoned, since they are all built on the very notions which are limiting data connectivity. A system of pure relations (SOPR) out of necissity needs to be completely different.

Terminology: Pile – invented by Erez Elul – is such a SOPR.1 It is built solely on the notion of relations. Relations are binary and directed: Pile relations always relate just two “things” (Fig 10).

basic_pile_relation.jpg

Pile objects (which are binary relations) can combine to form more complicated relations. Each relation is directed and has two parents, a «Normative parent» and an «Associative parent».

  • The emerging fundamental conceptual difference between Pile Objects and Multiple Forms is that Pile objects are built on spaces which are a priori unique and distinct (the «Terminal Values», TV’s) and they are described as «directed relations», whereas Multiple Forms are constructed always on the same (undistinguished) Void Space, and they are described as (multiple) Distinctions, which are -of course- also directed by virtue of their implicit distinction between inside and outside.

To verify that Multiple Form Logic expressions can also be regarded as «directed», observe that:

a_b__b_a2.jpg

So, there is an inherent direction which is clearly distinguishable in Multiple Form Logic: «A -> B» is not the same as the reverse implication «B -> A», or (in Multiple Form notation) «A#X,B» is not identical to «A,B#X».

Now, since directions are implicitly present in Multiple Form Logic, one might be tempted to assume that the «normative» Pile-parent is «inside», while the «associative » Pile-parent is «outside» the boundary (or form) that represents the relation itself:

a_b.jpg

However, this naive interpretation suffers from some drawbacks, which become evident when we try to represent a Pile-object such as:

pile_example.jpg

In this case, if we assume the «naive modelling» of Pile 0bjects (as previously outlined) we would end up with a Multiple Logic expression such as «A#X,B,C#X», which (due to commutativity in Multiple Forms) cannot be distinguished from the form «C#X,B,A#X», corresponding (according to this interpretation) to the Pile object:

pile_example2.jpg

However, in Multiple Form Logic, it is always possible to define «special distinctions», serving particular purposes. E.g. suppose we define three «special forms» to represent the Pile-properties of «normative», «associative» and «child». Suppose also that we use a colour-convention (for visualisation) where these special forms are depicted in Blue, Red, and Green colour. Piles objects can then be «modelled» in Multiple Form Logic as follows:

mf2pile3.jpg

Well, if this intepretation of Pile is adopted, then every Pile object in Multiple Form Logic becomes a triple which can become the constituent (parent)- relation of other Pile objects.

There also other possibilities for modeling the Pile System In Multiple Form Logic. For example, we could assume that the self-reference operator (normally assumed to be XOR for a Boolean interpretation) is not symmetric, i.e.

 

non_symmetric_xor.jpg

A#B =/= B#A.

It then becomes possible to represent Fig. 10 (the directed binary relation between A and B in «Pile») as follows:

basic_mf2.jpg

Of course, this is an arbitrary and speculative kind of interpretation. (The previous one, involving Blue, Red and Green distinctions, seems to be much better).

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