What will change and what will remain

This is a continuation of the two articles “What needs to be agreed upon” and “What can be disagreed upon”, in which two people have a discussion, after which a third party is invited to interpret a transcription of it. We have concluded that if the meaning of a posit is universally agreed upon, anyone is nevertheless at liberty to disagree or express doubt towards what it is saying. Opinions about posits are recorded in the transcript itself using assertions, a kind of meta-posit that assigns someone’s confidence level with respect to a posit.

Change is everywhere, and the last article concluded that both the circumstances that posits and assertions describe may change over time. Values change and opinions change. Let us make the transcript a living document, required to capture such changes. Additionally, the transcript much be historically complete, capturing the changes in a non-destructive manner. Anything that goes into the transcript is written in stone.

Grab your chisel, because Jennifer broke up with her boyfriend. Recall that the posit P1 is ({(J42, girlfriend), (B43, boyfriend)}, official, 2019), where J42 is Jennifer and B43 her boyfriend. The posit P3 tells us what happened in 2020 and it looks like this ({(J42, girlfriend), (B43, boyfriend)}, broken up, 2020). Remember the posit P2? It is ({(J42, nickname)}, Jen, 1988). Clearly, they are all different posits, P1 ≠ P2 ≠ P3, but P1 and P3 must share something in order for them to be describing a change that they do not share with P2.

It is actually possible to precisely define change. When two posits share the same set in their first position, but have different values and one time point follows the other, they describe a change. With that in place, P3 is obviously a change from P1. Since the set in P2 differs from that in P1 and P2, it is not a change of either P1 or P3. In #transitional modeling, the set is called a dereferencing set. They remain, indefinitely, while their surroundings may change entirely. Even after J42 is gone, the dereferencing sets in which that identity is found will remain, because we can, of course, have a recollection of things that are no more.

Then how does change affect assertions? Since assertions are posits themselves it works in exactly the same way. Jennifer made the following assertion on the 5th of April in 2019 ({(P1, posit), (J42, determines confidence)}, 0.8, 2019-04-05), stating that it is very likely that she and her boyfriend officially has been an item since 2019. After learning that her “boyfriend” thought otherwise, she changed her mind. Let’s say that they had a serious talk about this on the 21st of September 2019. Jennifer’s revised confidence in P1 can then be expressed through another assertion ({(P1, posit), (J42, determines confidence)}, 0, 2019-09-21). This assertion changes her previous confidence level from 0.8 to 0, so after the 21st she has no clue if they actually were an item or not.

Incidentally, this is how a ‘logical delete’ works in a bitemporal database. Albeit, in those databases there are only two confidence values, 1 (recorded) and 0 (deleted). The database itself is also the only one allowed to have an opinion. In other words, the functionality of a bitemporal database can be described as a small subset of #transitional modeling. When confidences are extended to the continuous interval [0, 1], the functionality approaches that of probabalistic databases. If further extended to include negative confidence, [-1, 1], we approach uncertainty theory, yet to be explored in databases. The fact that anyone may have an opinion is similar to multi-tenant databases. Transitional modeling as a formal base is very powerful, despite it’s simple construction.

Back in the shoes of the third party reading the transcript, we find the posit P4 as ({(S44, nickname)}, Jen, 1988). So, wait, what? There were in fact two different Jens after all, J42 and S44? What exactly is the thing with identity S44? This will be the topic of the next article, entitled “What we are”.

What can be disagreed upon

This is a continuation of the article entitled “What must be agreed upon”, in which two individuals have a discussion, whereafter a transcript appears that a third party is invited to interpret. The transcript consists of a number of posits, for example ({(J42, girlfriend), (B43, boyfriend)}, official, 2019) and ({(J42, nickname)}, Jen, 1988). The syntax of a posit is described as a triple, where the first position is occupied by a set of ordered pairs, each pair being an identity and a role. The set is followed by a value and time point, which both may be imprecise in nature. What must be agreed upon is the syntax of the posit and the semantics of what it expresses. That sums up the conclusions of the earlier article.

Given the title of this article, let us follow up by investigating disagreements, and here comes an important distinction. Even if you understand what a posit is saying, it doesn’t imply that you believe in what the posit is saying. Many different opinions are certainly held towards a statement such as “We are alone in the universe”. So, if we want to talk about posits in the language of #transitional modeling, the posit itself must be given an identity. To talk about ({(J42, girlfriend), (B43, boyfriend)}, official, 2019) we give it the identity P1 and ({(J42, nickname)}, Jen, 1988) will be P2. The identities make it possible to create new posits that talk about other posits; meta-posits if you like.

If posits that talk about other posits live alongside posits that talk about other things, we cannot allow for any confusion with respect to the roles. We will therefore reserve roles for our purposes, say the strings ‘posit’ and ‘determines confidence’. An assertion is a posit exemplified by ({(P1, posit), (J42, determines confidence)}, 0.8, 2019-04-05). The interpretation is that Jennifer (J42), since 2019-04-05, expresses a confidence of 0.8 with respect to if her girlfriend/boyfriend status with B43 was official since 2019 (P1). Similarly ({(P1, posit), (B43, determines confidence)}, -1, 2019-04-05). We will see that those confidence numbers reveal a big conflict!

Confidences, at lease those found in our assertions, fall within the [-1, 1] interval. The mapping between how something is expressed in natural language and the numerical confidence is fuzzy. But, let us assume that 0.8 corresponds to “very likely”. Then Jennifer is saying that it is very likely that B43 officially became her boyfriend in 2019. The twist in the plot is that the boyfriend is of a very different opinion. On the negative scale of confidences, certainty towards the opposite is expressed, and -1 is “completely certain of the opposite”. More precisely, this is equivalent to being completely certain of the complement of a value. In other words, the boyfriend is completely certain, with confidence value 1, of the posit ({(J42, girlfriend), (B43, boyfriend)}, anything but official, 2019).

Tucked in between is a confidence of 0, which we call “complete uncertainty”. Let us assume that the boyfriend is clueless, and instead asserted ({(P1, posit), (B43, determines confidence)}, 0, 2019-04-05). This is interpreted as the boyfriend having no clue whatsoever if P1 is a truthful posit or not. Perhaps memory is failing or the boyfriend chose to forget. Assertions with confidence give us a powerful machinery to express differences of opinon. To recap, confidence 1 means certain of one particular value, -1 certain it’s a value different from one particular value, and 0 that it could be any value whatsoever. Values in between express confidence to a given degree.

The first article mentioned the unlikeliness of Jennifer eternally being in a good mood. There will come a time when her mood is different. Likely when she finds out what her boyfriend is asserting. At that point, maybe the recollection of her boyfriend is better, and he changes his mind. Circumstances definitely change over time, but we haven’t yet seen change in action. This will be the topic of the next article, entitled “What will change and what will remain”.

The observant reader will notice that assertions here are slightly different from in the paper “Modeling conflicting, uncertain, and varying information”. There the assertion is an actual construct, a predicate, different from the posit. Here the assertion is a meta-posit built around a semantical reservation. The reasoning behind the different approach is that if assertions are expressed as posits, they can be talked about as well using another layer of posits; a kind of über-meta-posits.

What needs to be agreed upon

If we are to have a discussion about something there are a few things we first need to agree upon in order to communicate efficiently and intelligibly. A good way to test for what we need is to transcribe a discussion between two individuals and afterwards hand this over to a third non-participating individual, who should be able to unambiguously interpret the transcription.

Let’s say one of the individuals in the discussion frequently talks about ‘Jennifer’, while the other uses ‘Jen’. In order to avoid possible confusion, it should be agreed upon that ‘Jen’ and ‘Jennifer’ is the same person. This can be done by the introduction of a unique identifier, say ‘J42’, such that the transcript may read “I talked to Jen (J42) today.” and “Oh, how is Jennifer (J42) doing?”. We need to agree upon the identities of the things we talk about.

Assuming the respose is “Jen (J42) is doing good.” followed by “I figured as much, new boyfriend and all, so Jennifer (J42) must be good.”. In this case ‘good’ is a value that should mean the same thing to both individuals. However, ‘good’ is not scientifically precise, but there is a consensus and familiarity with the value that let’s us assume that both parties have sufficiently equal definitions to understand each other. Imprecisions that would lead to confusion could of course be sorted out in the discussion itself. If “Jen (J42) is doing so so.”, then “What do you mean ‘so so’, is something the matter?” is a natural response. We need to agree upon values, and that any imprecisions lie within the margin of error with respect to the mutual understanding of their definitions.

Now, if the transcription needs to be done efficiently, leaving out the nuances of natural language, that challenge can be used to test whether or not the two constructs above can capture the essence of any discussion. Using identities and values we can construct pairs, like (J42, Jen), (J42, Jennifer), (J42, good). Forget that you’ve heard anything and put yourself in the shoes of the third party. Apparently, something is missing. There is no way to tell what ‘Jen’, ‘Jennifer’, and ‘good’ are with respect to the thing having the identitiy J42. This can be sorted out by adding the notion of a role that an identity takes on with respect to a value. Using roles, the pairs become triples (J42, nickname, Jen), (J42, first name, Jennifer), and (J42, mood, good). We need to agree upon the roles that identities take on with respect to values.

Surely this is enough? Well, not quite, unless Jen is permanently in a good mood. The triple (J42, mood, good) is not temporally determined, so how could we tell when it applies? The third party may be reading the transcript years later, or Jen may even have broken up with her boyfriend before the discussion took place, unbeknownst to the two individuals talking about her. Using a temporal determinator, interpretable as ‘since when’, the triples can be extended to quadruples (J42, nickname, Jen, 1988), (J42, first name, Jennifer, 1980-02-13), and (J42, mood, good, 9.45 on Thursday morning the 20th of August 2019). The way the point in time is expressed seems to differ in precision in these quadruples. Actually, there is no way to be perfectly precise when it comes to expressing time, due to the nature of time and our way to measure it. It’s not known exactly when Jennifer got her nickname Jen, but it was sometime in 1988. We need to agree upon the points in time when identities took or will take on certain roles with respect to certain values, to some degree of precision.

This is almost all we need, except that the quadruple can only express properties of an individual. What about relationships? Let B43 be the identitiy of Jen’s boyfriend. We may be led to use a quadruple (J42, boyfriend, B43, 2019), but this has some issues. First, B43 is in the third position, where a value is supposed to be, not an identity. If we can overlook this, the second issue is more severe. Can we really tell if B43 is the boyfriend of J42 or if J42 is the boyfriend of B43? The way we introduced the role, as something an identity takes on with respect to a value, the latter alternative is the natural interpretation. Finally, the nail in the coffin, relationsships may involve more than two identities. Where in the quadruple would you put the third party?

The solution is to return to a triple, but where the first position contains a set of ordered pairs ({(J42, girlfriend), (B43, boyfriend)}, official, 2019). This resolves the issue of who is the boyfriend and who is the girlfriend. The second position is again a value and the third is the temporal determinator. Looking back, we can actually consolidate the quadruple used to express properties to a triple as well ({(J42, nickname)}, Jen, 1988). The only difference being that the cardinality of the set is one for properties and more than one for relationships. Triples like these are called posits in #transitional modeling.

We could leave it here and be able to represent a whole lot of information this way. But, let us return to the three individuals we have been talking about. Now that the transcript is in place, consisting of a number of posits, what if they cannot agree upon it being the single version of the truth? What if some of what was written down is not 100% certain? What if someone is of an opposite opinion? This sounds like important information, and it can actually easily be transcribed as well, but it requires another construct, the assertion. This will be the topic of the next article; “What can be disagreed upon”.

Screw the Hammer

About 500BC the greek philosopher Heraclitus said “Panta Rhei”, which translates to “everything flows”. The essence of his philosophy is that if you take a thing and examine it at two different points in time, you can always find something that changed in between the two. This thinking is at the heart of transitional modeling, in that not only does it capture the changes a thing has undergone, but also changes to the interpretation of the examination (making it bitemporal). Furthermore, while a thing is an absolute, an examination is relative to the one performing it. In transitional modeling concurrent and possibly conflicting opinions are allowed. Finally, examinations may lead to imprecise results or there may be uncertainty about the examination process. Both imprecision and uncertainty are well defined and representable concepts in transitional modeling. 

I believe that even if you are not facing requirements that fits the above, yet, you will benefit from understanding the concepts of transitional modeling. Given some screws and a hammer it is way too easy to let the tool decide the solution, which is precisely what has been going on with database modeling.

Many features of transitional modeling can be found in our concurrent-reliance-temporal Anchor modeling. Why not take it for a spin in the online modeling tool?

http://anchormodeling.com/modeler/latest

Schemafull Databases

Over the last decade schemaless databases have become a thing. The argument being that too much work is required at write time conforming information to the schema. Guess what, you only moved that work higher up the information refinery. In order to digest the information, it will at some point have to conform to some schema anyway, but now you have to do the work at read time instead. Would you rather spend additional time once, when writing, or spend additional time every time you read? You may also have heard me say that ‘unstructured data is just data waiting to be structured’.

That being said, there is a huge problem with schemas, but the problem is that information needs to be stored according to one rigid schema, rather than alongside many flexible schemas. The rigidity of current schema based databases often leave us no option but to peel and mold information before it fits. Obviously, discarding and deforming information is bad, so I do understand the appeal of schemaless databases, even if they fail to address the underlying issue.

The only way to store the bananas above in my stomach are to peel them and mold them through my mouth, acting much like a relational database with a particular schema. The relational database forces me to do a few good things though, things not always done in schemaless databases. Identification has to be performed, where bananas are given identities, so that we know if this is a new banana or one that is already in the stomach. Thanks to things having identities, we can also relate them to each other, such that all these bananas at one point came from the same bunch above.

Another advantage of identities, along with the ability to relate these to the identities of other things and their properties, is that we can start to talk about the things themselves. Through such metaspeak it is possible to say that a thing is of the Banana type. With this realization, it is hard to understand why a schema should be so rigidly enforced, unless metaspeak is assumed to be autocratically written in stone, while at the same time being univocal, all-encompassing, and future proof. How true does that not ring to someone living in the real world?

No, let there be diversity. Let us take the good things from relational databases, such as identification and the possibility to express relationships as well as properties, but let us not enforce a schema, taking the best part of the schemaless databases as well. Instead, let there be metaspeak expressed using the same constructs as ordinary speak, and let this metaspeak be spoken in as many ways as there are opinions. Let us talk about #schemafull databases instead!

A #schemafull database is one in which information is stored as pieces of information, posits, each tied to a an identified thing, and opinions about these pieces, assertions, made by some identified thing. What class of things a particular thing belongs to is just another piece of information, about which you may be certain to a degree, hold a different opinion than someone else, or later change your mind about. These pluralistic “schemas” live and indefinitely evolve alongside the information. There is neither no limit to how much additional description these classes and schemas can be given. They could, for example, be parts of different (virtual) layers, such as logical or conceptual, or they could be related hierarchically, such that a Banana is a Fruit.

Surely though, if we are to talk about a things and have a fruitful conversation, must we not agree upon something first? We do, of course, and what we believe to be the least to be agreed upon are necessarily identities and roles, and presumptively values. As an example, looking at the posit “This banana has the color yellow”, everyone who asserts this must agree that ‘this banana’ refers to the same thing, or in other words uniquely identifies a particular thing. The role of ‘that having a color’ must have the same meaning for everyone, in how it applies and how it is measured. Finally, ‘yellow’ should be as equally understood as possible.

The reason the value part is less constrained is simply because not all values have a rigorous definition. The color yellow is a good example. I cannot be sure that your yellow is my yellow, unless we define yellow using a range of wavelengths. However, almost none of us run around with spectrometers in our pockets. The de facto usage of yellow is different, even if we can produce and measure it scientifically. We will therefore presume that for two different assertions of the same posit “This banana has the color yellow”, both making those assertions share an understanding of ‘yellow’. There is also the possibility of representing imprecision using fuzzy values, such as ‘yellowish’, where ‘brownish’ may to some extent overlap it.

It is even possible to define an imprecise Fruitish class, which in the case of the Banana may be a good thing, since bananas botanically are berries. It’s also important to notice the difference between imprecision and uncertainty. Imprecision deals with fuzzy posits, whereas uncertainty deals with fuzzy assertions. It is possible to state that “I am certain that Bananas belong to the Fruitish class”, complete certainty about an imprecise value. Other examples are “I am not so sure that Bananas belong to the Fruit class”, uncertainty about a precise value, and “I am certain that Bananas do not belong to the Fruit class”, complete certainty about the negation of precise value.

A database needs to be able to manage all of this, and we are on our way to building one in which all this will be possible, but we are not there yet. The theory is in place, but the coding has just started. If you know or can learn to program in Rust and want to help out, contact me. You can also read more about #transitional modeling in our scientific paper, and in the articles “Schema by Design“, “The Illusion of a Fact“, “Modeling Consensus and Disagreement“, and “The Slayers of Layers“. Don’t miss Christian Kaul’s “Modeling the Transitional Data Warehouse” either, in which conflicting schemas are exemplified.

There is also an implementation of #transitional modeling in a relational database, of course only intended for educational purposes. The rigid schema of which can be seen below…

Stop peeling and molding information and start recording opinions of it instead. Embrace the schemas. Embrace #transitional modeling. Have a banana!

The Illusion of a Fact

It is funny how limitations, when they have been around for a while, can be turned into beliefs that there is only one way of thinking. The right way. This is the case of databases and the information they store. We have been staring at the limitations of what databases can store for so long that we have started to think that the world works in the same way. Today I want to put such a misconception to rest. Databases store facts, so naturally we look for facts everywhere, but the truth is, in the real world there are very few facts.

The definition of a fact is “a piece of true information” and “things that are true or that really happened, rather than things that are imaginary or not true” according to the MacMillian dictionary. Let me then ask you, what do you know to be true? It is a fact that “the area of a square with the side x is x squared”, however, limited to squares on a euclidean plane. Mathematics, as it turns out, is one of the few disciplines in which we actually can talk about truth. This is not the case for science in general though.

Is the statement “There are no aliens on the dark side of the moon” a fact? You would, if asked if there are aliens on the dark side of the moon, probably answer that there are no aliens there. However, if you were pushed to prove it, you may think otherwise. The reasoning would be that there is this extremely miniscule chance there could be something alien there. We could leave it at that and disqualify the statement as a fact, but let’s not just yet. What is more interesting is why you are almost sure it is a fact.

Back in days of the ancient greeks, Aristarchus of Samos suggested that the Earth revolves around the Sun. Heliocentrism was then forgotten for a while, but brought back by the brave Galileo Galilei almost 2000 years later. You have to rely on these guys being right to begin with, and that the moon is not painted on the sky or made of cheese. Then, you have to rely on the Apollo 8 mission, in which astronauts actually observed the dark side. The photographs that were taken further imply that you rely on the science behind imagery and that any images have not been tampered with. You need to rely on that aliens do not have cloaking devices, or that aliens in generals seem unlikely, and that any claimed observations are not made by credible sources.

You can build a tree view of all the things you rely on in order to feel assured that there are no aliens on the dark side of the moon. I just need to put one of them in doubt for the fact to become a non-fact. This illustrates how fragile facts are, and that they therefore constitute a small small small minority of the information we manage on a daily basis. Yet, for the most part we continue to treat all of it as facts.

For this reason, in transitional modeling, the concept of a fact is omitted, and replaced by a posit. A posit has no truth value at all and is merely a syntactical construct. Assuming “There are no aliens on the dark side of the moon” is a posit just means that it is a statement that fits a certain syntax. In order for such a statement to gain meaning and some kind of truth value, someone called a positor must have an opinion about it. A second construct, the assertion, semantically binds a posit to a positor, and expresses the degree of certainty with which the positor believes the statement to be true or not true. Together they express things like ‘Peter the positor is almost completely sure that “There are no aliens on the dark side of the moon”‘. Concurrently it may also be the case that ‘Paulina the other positor thinks there is a slight chance that “There actually are aliens on the dark side of the moon”.

Information, is in this view factless and instead has two parts, the pieces of information (posits) and the opinions about the pieces (assertions), better representing its true nature. That two such simple constructs can lead to a rich theory, from which other modeling techniques can be derived as special cases, such as Anchor modeling, Data Vault, and the third normal form, may be a bit surprising. Read more about it in our latest scientific paper, entitled “Modeling Conflicting, Uncertain, and Varying Information”. It can be read and downloaded from ResearchGate or from the Anchor Modeling homepage.

Schema by Design

Lately, there’s been a lot of talk about when a schema should be applied to your data. This has led to a division of databases into two camps, those that do schema on write and those that do schema on read. The former is the more traditional, with relational databases as the main proponent, in which data has to be integrated into a determined schema before it can be written. The latter is the new challenger, driven by NoSQL solutions, in which data is stored more or less exactly as it arrives. In all honesty, both are pretty poor choices.

Schema on write imposes too much structure too early, which results in information loss during the process of molding it into a shape that fits the model. Schema on read, on the other hand, is so relaxed in letting the inquiring part make sense of the information that understandability is lost. Wouldn’t it be great if there was a way to keep all information and at the same time impose a schema that makes it understandable? In fact, now there is way, thanks to the latest research in information modeling and the transitional modeling technique.

Transitional modeling takes a middle road between schema on read and schema on write that I would like to call schema by design. It imposes the theoretical minimum of structure at write time, from which large parts of a schema can be derived. It is then up to modelers, which may even disagree on classifications, to provide enough auxilliary information that it can be understood what the model represents. This “metainformation” becomes a part of the same body of information it describes, and abides by the same rules with the same minimum of structure.

But why stop there? As it turns out, types and identifiers can be described in the same way. They may be disagreed upon, be uncertain, or vary over time, just like information in general, so of course all that can be recorded. In transitional modeling you can go back to any point in time and answer an inquiry as it would have been answered then and from the point of view of anyone who had an opinion at the time. Actually, it does not even stop there, since constraints over the information, like cardinalities, also are respresented in the same way. It all follows the same minimum of structure.

What then is this miraculous structure? Well, it relies on two constructs only, called posits and assertions, both which are given proper treatment in our latest scientific paper, entitled “Modeling Conflicting, Unreliable, and Varying Information”. It can be read and downloaded from ResearchGate or from the Anchor Modeling homepage. If you have an interest in information modeling, and what the future holds, give it an hour. Trust me, it will be well spent…

Transitional Modeling

Our latest paper is now available, entitled “Modeling Conflicting, Unreliable, and Varying Information”, in which Transitional Modeling is formalized. It can either be viewed and referenced on ResearchGate or downloaded directly from here. Much of what is found in the paper has been part of our courses since we began certifications, and is also available in the online course, but new research from the last couple of years has also been added.

ABSTRACT
Most persistent memories in which bodies of information are stored can only provide a view of that information as it currently is, from a single point of view, and with no respect to its reliability. This is a poor reflection of reality, because information changes over time, may have many and possibly disagreeing origins, and is far from often certain. Hereat, this paper introduces a modeling technique that manages conflicting, unreliable, and varying information. In order to do so, the concept of a “single version of the truth” must be abandoned and replaced by an equivocal theory that respects the genuine nature of information. Through such, information can be seen from different and concurrent perspectives, where each statement has been given a reliability ranging from being certain of its truth to being certain of its opposite, and when that reliability or the information itself varies over time, changes are managed non-destructively, making it possible to retrieve everything as it was at any given point in time. As a result, other techniques are, among them third normal form, anchor modeling, and data vault, contained as special cases of the henceforth entitled transitional modeling.

We hope you all will have fun with transitional modeling, as our research continues, particularly with respect to how it should fit into a database, relational or not.