Transitional Modeling aims to capture the ongoings of real life events in a
simple but powerful format, while minimizing information loss as such events
are recorded. At its core it talks about things and the multifaceted situations
these things appear in. Things are represented by unique identifiers,
such as 42 and 89. When a thing
appears in a situation it does so by taking on roles, such as
loves and beloved. It is
necessary that anyone who has an opinion about the situation agree upon
which unique identifiers correspond to which things and the meaning of the
roles. This necessary agreement ensures that whatever unique identifiers and roles
represent are interpreted equally for every involved party regardless of when,
where, or how interpretations are made.
Together, identifiers and roles can be used to form appearances:
(42, loves) and (89, beloved).
Technically, an appearance is an ordered pair, consisting of an identifier for a thing
and a role this thing has appeared or will appear through. From the example it can be determined
that the thing represented by 42 has at some point appeared as one who
loves something and 89 as a thing
beloved. Given this, it is still undetermined who 42loves and by whom 89 is beloved.
In order to relate the things to each other an appearance set is needed, such as
{(42, loves), (89, beloved)}. Only then can we know that
42loves89 and that
89 is the beloved of 42.
When a thing appears to have a certain property, rather than
a relationship to other things, the appearance set will only contain one appearane, such as
(42, has name). An appearance set has one or more appearances as members and it provides the base upon
which we can bestow a value.
While 42 and 89 have become forever and uniquely bound to the things they represent,
experience tells us that loves and beloved may be transitional states. An accurate
description needs to qualify or quantify the relationship using an appearing value, such as actively felt, and
an appearance time, such as , indicating since when this value has been in effect.
All together these form a posit:
A posit binds an appearance set to an appearaing value at an appearance time. We now know that
42loves89, 89 is the beloved of 42, and it is actively felt since
. However, such knowledge relies on every posit being confidently and unquestionably true. It is therefore
frail knowledge, since it fails to capture the inherently uncertain and conflicted nature of information. Anything built upon frail knowledge
may come down crashing when reality makes itself heard and the gaps prove unfillable.
The solution is to
explicitly make it possible to express doubt and disagreement about posits, instead of assuming them to be
confidently and unquestionably true.
Let us assume that 89 thinks it very likely that 42loves89 since , and that this thought was
expressed on . As we may want to prevent individuals from contradicting themselves, the
certainty they express towards a posit must be put into numbers, and more specifically into the [–1, 1] interval. This will
provide us with the capability to mathematically decude if contradictions exist. So, let the notion of "very likely" correspond
to a certainty in the interval 0.7 – 0.8. This is no exact science, which is why an
imprecise value in the form of an interval is used. Regular values may also be imprecise,
so there needs to be a presumed agreement among the involved parties with respect to reliabilities and values.
If two individuals both talk about actively felt we will presume they share an equal interpretation,
even if the value itself implicitly expresses some degree of imprecision. Similar reasoning apply to points in time, which
are by their very nature impossible to capture with infinite precision.
Given that we now know how 89 expressed themselves, with respect to an existing or at the time of
expression newly created posit, an assertion can be formed, such as:
An assertion is in itself a posit, using the two reserved roles ascertains and posit.
In order for 89 to express an opinion about a posit, the posit must also be associated with a unqiue
identfier, here 555. Assertions are meta-posits, and they provide additional context to a posit
in the form of how certain some thing deems it to be at some point in time. The appearance time of an assertion is
also called assertion time.
Thinking about it some more, 89 became completely certain of the posit. Reconsideration can be captured through
a new assertion, with a later assertion time, here .
Certainty is also transient, people change their minds all the time. That this is indeed a change can be determined
by the fact that: two posits have the same appearance set but different values at different appearance times. The assertion
in effect is different depending on what time it is.
Just like the assertion in effect can change, so can the original posit.
[{(42, loves), (89, beloved)}, "felt no longer", '2011-11-11']
Since this posit is different it will be associated with a new unique identfier. This posit indicates a change, but given
that we still haven't seen any assertions, we do not know if this is actually how 42 and 89
feels. They express their opinions of the new posit 556 in the following assertions.
While 89 is certain of the posit, 42 is certain it's not the case. This is an example of
a concurrent disagreement between the two asserters. Perhaps 89 fell out of love, while
42 did not.
People do err sometimes though. Not long after, 89 realizes their mistake and needs to somehow mend
the whole situation, and expresses the following.
The first assertion has a certainty of 0, complete uncertainty, also known as a retraction. Since
89 has no opinion at all about the posit 556. Instead, 89 restates their
opinion towards 555. A posit is a restatement if for the same appearance set, the value is the same as
in the immediately preceding posit with respect to their appearance times.
To summarize, posits are statements that are opinionated through assertions, where the assertions themselves are also expressed
as posits. Certainty ranges from being certain something is completely inaccurate to it being completely accurate, with
complete uncertainty midway between, which is the same as having no opinion at all. Information may change over time, where
a change is identified by two posits with the same appearance set, but different values at different times.
If a body of information was to be expressed using Transitional modeling, or in other words, with posits, the following types
of searches could be performed:
✔︎ Search anywhere for the unique identifier 42, NVP Database-like search.
✔︎ Search apperances for the beloved role, Graph Database-like search.
✔︎ Search for every time (89, beloved), Graph Database-like search.
✔︎ Search for when beloved is actively felt, Relational Database-like search.
✔︎ Search for information as it was on , Temporal Database-like search.
✔︎ Search for information given what we knew at , Bi-Temporal Database-like search.
✔︎ Search assertions for disagreements between 42 and 89, Multi-tenant Database-like search.
✔︎ Search for information that is at least 0.75 reliable, Probabalistic Database-like search.
✔︎ Search for corrections made between and , Audit Database-like search.
✔︎ Search for how many times consensus on a posit has been reached, new feature search.
✔︎ Search for how many times opposite opinions have been expressed, new feature search.
✔︎ Search for individuals that have expressed themselves contradictory, new feature search.
Further reading
If you would like some more in-depth discussions on the topics in the summary, the following posts are suggested
reading: