Low cost technology
This implementation is based on modern modal logic and then Scalable Vector Graphics (SVG) are the ideal means to visualize causality as directed acyclic graphs. SVG is an XML-based vector image format for encoding two-dimensional images.
For use on a digital platform Scalable Vector Graphics (SVG) an XML-based vector image format for defining two-dimensional graphics has been chosen. To be scalable means to increase or decrease uniformly. In terms of graphics, scalable means not being limited to a single, fixed, pixel size.
SVG files have the same facilities as a webpage, a .html file. Images of other formats such as .gif and .png can be easily embedded. You can even embed video as <foreignObject>. See this example.
Although SVG was already defined for the first time by WC3 in 2008 and the second version dates from 2011 (Dahlström et al., 2011), it’s use is still limited because most social media platforms do not allow the upload of SVG images, though it is often used in scientific research. But this is not a restriction for teachers, lecturers and students, that can make or coordinate their own knowledge base using structured directed analytic graphs. Datalog might be an application to store and share the data of these directed analytic graphs.
The use of directed graphs as visualization of scientific evidence is not new; there are numerous applications of this. For example, in biology, in anthropology, medical sciences and accident analysis. In the first three examples with the function of illustration, in the last example, however, as a diagram for a proof. What is new in this concept is (1) the use of SVG that allows (2) image and text to be used together in an XML file with a unique URL and (3) the text in it to be directly linked to with at least three links to texts in which the analytical evidence is displayed.
The directed graphs in the SVG image represent the structure of the proof, based on modal logic and using disjunctive Horn Clauses. This grammar is "context free" i.e. independent of the meaning of the text or terms used in those Horn Clauses. For those terms to be linked to their meaning and its context, they must be linked to their context in natural language. In our proposal, this is not only a necessity but also an obligation. Otherwise, the proof is meaningless. We also propose that those documents in natural language should faithfully display the sources of the discourse used there and use only academic literature as sources. The sources should also be noted
[back to the top of the page]Scope and the limits of various speeds, timescales and places
The proposal can only be used for discrete processes. The transition from one state to another should be measurable and at least one threshold value should be measurable, or at least unambiguously ascertainable, that explains the transition from one state to another.
Based on the experience when developing the entire water cycle with graphs, one can say that it gets tricky when assembling complex processes, meaning when a process is running within another process. Not to say it is impossible to implement, but is gets tricky. For now I propose to use it only for single complex processes and their concatenation.
The main reason for that difficulty are the speeds and timescales of those processes varying from each other. For instance we know that climate science is not the same as meteorology. But also the thermodynamics of clouds, for instance the multiple movements of water drops and ice crystals of 20μm, have a different speed and time frame compared with the probability of the actual falling of water through the cloud base when they reach 200μm, what we call the weather being studied by hydrology. In all cases, speed and timeframe are an indispensable part of the analysis.
When using Prolog for evaluation all terms must be unique. It is preferred then to use Prolog terms for the headers to guarantee uniqueness.
Moreover, we cannot visualise chaos theory either, even though it may contain a ground of truth. That a butterfly's wing beat in the Amazon can cause a thunderstorm in Tanzania is not proven until every process in that chain has been demonstrated. So it is also important to respect the unity of space, speed and time.
When Prolog is used for evaluation, all terms must be unique. It is then preferable to use Prolog terms for headers.
[back to the top of the page]Application of Directed Graphs
Directed graphs are used in this concept as a math without numbers. This doesn't mean it can't be used with numbers. In various research domains, weighted directed graphs are used as an analysis method of datasets, in search of causal relationships, 'causal discovery'. However, the causal relationships depicted in this concept are based on proven scientific facts, the graphs themselves are not proofs but they are a tool for depicting proofs.
The components of this directed graph are at least two nodes, connected by a directed arrow. The simplest application is connecting two facts, statuses (the nodes) with a causal process (the arrow). We call this a causal triplet. The node consists of at least two parts: (1) the formulation of a fact, state or process and (2) the condition(s) that are the basis for the occurrence of this fact, state or process. These conditions may be the result of measurements or observation or both. This observation can also be the definition of a process. A stable state of living organisms is the result of a cyclic process.
We use "OR" in natural language but logically it is meant the measurements and observations bust be true all at the same time, thus logically they are connected with the conjunctive "AND" operator. It goes without saying that these expressions will contain numbers and mathelatical expressions.
For these definitions Prolog terms are used for now. Prolog is a programming paradigm for logically programming, using Horn Clauses. You can see an example uf such a Prolog program here. However, these Prolog terms are not an obligation because for SVG it is just undefined "text". It is a recommended practice to provide extensive definitions in natural language for the short formal definitions in the graphs anyway.By extension, the semantics of these definitions could be based on a Resource Definition Framework
The use of this Prolog terms has the advantage of standardizing the expressions and using these terms they can be stored in a database of facts, states and processes, that can be consulted with great precision. The single words of the Prolog terms can also be translated more accurately than more verbose expressions and sentences. Here numbers are smuggled back into the causal logical concept, but encapsulated as "text", not to be processed. They are of course indispensable for formulating the conditions.
Two simple examples:
The first example is a singular triplet. One can ask why there is sstatistical graph in this example. Strictly logically it is indeed unnecessary, but it shows that the shrinkage of the polar ice cap is not linear, but proceedes wiht highs in the summer and lows in the winter. However, a clear decline is noticeable. This is the difference between logical relevance and didactic relevance. Since this proposal is intended as an educational tool, additional image information may be illuminating. It is a recommended practice to provide textual explanations of the formulas of the statusses and processes of the graphs. See for more definitions and contextual information of that graph.
The second example is a group of four triplets interconnected.
You find the definitions of the start status and de end status together with the conditions that makes them necessary in the nodes. Concerning the conditions the priciple of “conditio sine qua non” is used as it was proposed by Alexander Stepanov (Stepanov, 1985). It is impotant to notice that statistical correlation do not offer a necessary and sufficient condition. (Jacques Tacq, 1982; Ines Lee, 2021)
The stated conditions for a given fact or state must always be true at the same time. So they are connected by the logical “AND”. In the node of the graph they are listed one below the other in a table.
No conditions are indicated for the processes enclosed between two states. In principle these are defined by the conditions formulated in the parameters of initial_state and final_state. If required, conditions can be formulated, in the event that the process can only exist under those certain conditions, independent of initial_state and final_state.
A complex example can be found below with soil infiltration.
See also the galleria of the complete watercycle (Text is Dutch).
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Application of Hyperlinks in Directed Graphs using xlink:href
The visualisation of Directed Analytic Graphs is implemented using SVG defined in the Document Object Model (DOM) of XML . XML is a member of the Semantic Web. There you also find the definition of Xlink:href.
Xlink is defined as XML. Since the graphs will be stored in saperated files with extension .svg, they ougt to be coded as object as follows: <object data="uri" type="image/svg+xml" typemustmatch></object>. Therefore when using xlink:href in the .svg files a target must be specified like: target="_blank", target:="_parent" or target:="name". If not the linked content will be opened in the space assigned to the object.
The xlink:href is meant to point to supporting proof material. This can be provided in textual format, in graphic format of in a combination of both. This can be mentioned in the xlink:href with the attribute "rel": rel="external" or rel="search".
The textual material should be HTML or XML, having an external target. It can be activated from all the elements of the directed graph. The source of this textual material must be certified from an encyclopedia (e.g. the English Wikipedia), from a scientific institute (e.g. the ESA climate agency) or created by a teacher or scholar. A “measurement system analysis” is the strictest form of certification.
[back to the top of the page]Exclusive Disjunction of processes
An initial state can lead to different end states depending on a certain condition. In that case, different arrows will depart from that initial state to those end states of which at least one condition must differ in both end states. This is an EXCLUSIVE disjunction of processes. In this analytical concept of causality, the “INCLUSIVE disjunction” (or one or the other or both) NOT USED. This is a causal contradiction. For example, one can say that it sometimes rains, or sometimes snows, but never at the same time.[back to the top of the page]
Conjunction of processes
A complex process can be analyzed as being the result of different processes that together are simultaneously necessary for that complex process. Here you can speak of a conjunction of separate processes. So there will be different arrows departing from that process. This is then a CONJUNCTION of processes. You can clearly see this in this example of the photosynthesis process.
Application on facts and statussen
Facts and stausses are structurally approached in the same way in this concept, but are substantively different. Status is used in this concept as a measurable and/or observable category of facts that are part of the same set of events. An example: rain shower, snow, drizzle, hail are part of the same collection of precipitation. Since precipitation is observable and measurable, it can be approached conditionally as an umbrella category. The days-long downpour from which up to 100 liters per square meter fell in July 2021 in the Vesdre river basin in Belgium is an event. That wasn't drizzle. Strictly speaking, it also belongs to the precipitation category, but the causes of this individual fact will be looked at differently than the general precipitation category. Intensity and duration are indeed relevant here.
In summary. Statusses have common properties whose thresholds are measurable and/or observable. At the transition of one status to an other status, a process is the cause of the crossing of at least one of the thresholds of these statusses. The duration of that process can be a millisecond, but for example in the case of the formation of rain clouds also nine days. It takes an average of nine days before rain falls from a cloud formed above the oceans. In a historical context, these processes can take years and centuries. Climate change took longer than a day, week or year. It is a process that has been going on for some 200 years.
The desired level of knowledge depends on the type of knowledge one aims for, general knowledge about precipitation, or specific knowledge about a specific precipitation on a certain day, a certain hour, in a specific place. The first is material for secondary education, the second is knowledge that meterologists and hydrologists must have. The general rules that apply to a categorial status cannot be applied on separate events, but structurally they can be analyzed in the same way. These general rules do indeed apply to that event, but they are insufficient to explain its specificity.
[back to the top of the page]References
Dahlström, Erik et al, (2011) Scalable Vector Graphics (SVG) 1.1 (Second Edition), W3C Recommendation 16 August 2011, <https://www.w3.org/TR/2011/REC-SVG11-20110816/>
Lee, Ines (2021). 4 Reasons why Correlation does NOT imply Causation, Published in Towards Data Science"
Menzies, Peter, (2019), Counterfactual Theories of Causation, 29 October 2019, Stanford Encyclopedia of Pholosophy, <https://plato.stanford.edu/entries/causation-counterfactual/>
Mubayi, Anuj, Christopher Kribs, Viswanathan Arunachalam, 2019, Studying Complexity and Risk Through Stochastic Population Dynamics: Persistence, Resonance, and Extinction in Ecosystems, January 2019, Handbook of Statistics, DOI:10.1016/bs.host.2018.11.001, <https://www.researchgate.net/publication/330251417_Studying_Complexity_and_Risk_Through_Stochastic_Population_Dynamics_Persistence_Resonance_and_Extinction_in_Ecosystems>.
Reed, Stephen K. (2012). Cognition : theories and applications. Wadsworth, Cengage Learning, 12 April 2012, ISBN 978-1-133-49228-3. OCLC 1040947645, <https://www.worldcat.org/nl/title/1040947645>
Rottman BM, Hastie R. Reasoning about causal relationships: Inferences on causal networks. Psychol Bull. 2014 Jan;140(1):109-39. doi: 10.1037/a0031903. Epub 2013 Apr 1. PMID: 23544658; PMCID: PMC3988659. <https://pmc.ncbi.nlm.nih.gov/articles/PMC3988659/>.
Runge, Jakob, et al. , (2019), Detecting and quantifying causal associations in large non-linear time series datasets. Sci. Adv.5,eaau4996 (2019). DOI: <https://www.science.org/doi/10.1126/sciadv.aau4996>
Stepanov,
Alexander (1985), Towards a Theory of Causal Implication, Department of Electrical Engineering and Computer Science, Polytechnic University of New York, 1985,
<http://stepanovpapers.com/TOWARDS%20A%20THEORY%20OF%20CAUSAL%20IMPLICATION.pdf> Tacq,Jacques (1982), Causaliteit in sociologisch onderzoek, Sociologische Gids, RUG, Groningen
Disclaimer
These examples of analytic directed graphs serve only to illustrate the possibilities of the concept. The explanatory texts are taken from the Wikipedia. In fact, the concept is only really workable if there is an interdisciplinary team working on and monitoring the consistency, completeness and precision of the causal relationships and the underlying explanations. The causal relationships represented by it must start from empirically proven scientific facts. The graphs themselves are not evidence but a tool to present scientifically assumed evidence.
Author: Daniel Verhoeven