Triplets for Causation & Sequential Action Graphs

Math without numbers

Directed graphs are used in this concept as mathematics without numbers. This is not to say that it cannot be used with numbers. Weighted directed graphs are used in several research domains as an analysis method of datasets, looking for causal relationships, 'causal discovery' (Runge,2019).

This concept shares the the modal logic on which 'causal discovery' is based. In an article on PupMed that logic is discribed in detail. A proposal to link 'causal discovery' to an ontology is also found in that paper. Interactively Mapping Data Sources into the Semantic Web . The problem with that automatic clutch is that it is often ambiguous.(Rotman, Heisty, 2013).

In this concept, that's not a problem. Nothing is automatically generated, but the graphs are created by people who know the subject inside and out: researchers, lecturers, and other experts who know what they're doing. A machine doesn't know what it is about.

De causal relations that are visualised in this concept, are based on knowledge that has been proven and accepted by the science community. The graphs are not a proof but a tool to visualise proofs. The concept can only be used for discrete processes. The transition from one state to another should be measurable and at least one threshold should be measurable that explains the transition from one state to another.

Concise discription of EDAG, Elucidative Directed Analytic Graphs (*)

The general structure of EDAG is: measurable state -> process -> measurable state. When confronted with complex processes: measurable state -> process -> process -> process -> measurable state.

The use of directed graphs as visualisation of scientific evidence is not new; there are numerous applications of it. For example in biology, in de anthropology, de medicin and the analysis of causation of accidents. But sometimes these applications do not take into account the rules of the of modal logic, and these schemes are not unambiguous. To ensure unambiguity the production of those graphs in the concept is linked to a logical proof in Prolog, which in turn can serve as a consultable semantic database (Wielemaker,2005).

Also new in this application is the detailed and explicit use of Scallar Vector Graphs (SVG) that gives the possibility to
(1) integrate images and text fluently,
(2) integrate images in images, admitting meaningful diagrams.
(3) One can retrieve the images, save and scale etc.
(4) From each node and arrow, a Uniform Resource Locator (URL) can point to an explanatory text.
(5) That way, you turn your SVG into a semantic database of texts and images.
(6) An SVG can also be embedded in the explanatory text, allowing you to create a layered explanation system.
(7) The latter offers the opportunity to take an interdisciplinary approach to a problem.

SVG has the same facilities as an .html web page. CSS can be used to customise the layout. If you want to make an assignment for students, you can use CSS to make a section, a node or an arrow, disappear (albeit without actually letting it disappear) via its identifier and the property display:none in CSS.

The SVG diagrams can be displayed on a digital board and put online. The dual-coding theory of cognition claims that the human brain processes information using two different channels: a verbal and a visual one. Reed claims that using both channels improves memorisation.(Reed, 2012). A list of references about causal learning you can find here and hier.

The elements of a directed graph are minimal to nodes, connected by directed arrow. The most straightforward application is to connect two objects, facts, states (the nodes) with a causal process (the arrow). This is called a causal triplet.

Each node consists at least of two parts: (1) a header identifying an object, fact status or process (2) The formulation of the condition(s) underlying the occurrence of this specific fact, state, or process. These conditions must always be the result of measurements, observations, or both.

The text in the several parts of the graph can be a prolog term or plain text. The prolog terms have the advantage of being usable for queries, but it is ultimately the logical structure of the declarations that allows them to be transformed into a directed graph. When using plain text only sentence at a time per part That sentence must start with a capital letter and end with a point.

In the nodes of the graph, you'll find the definitions of the initial and final states, and the definition of the process is shown near the arrows. Below the definitions of the initial and final states, the conditions for reaching that state are listed. The principle of the "conditio sine qua non" is used here.

The given conditions defining a fact or state must always be true at the same time. Thus they are connected with the “AND” operator. In the node they are hold together by a table.

This example consists of just one triplet, but the concept is meant to represent complex processes with many to many triplets interconnected.

It is essential to add a summary discribing step by step the causal relations in natural language.

Points of interest

(1) Unlike in formal logic, in modal logic there is an additional dependent relation between cause and effect, the 'conterfactual dependence'. If Z is not also counterfactually dependent on X, there is no transitivity according to most logicians. If not, we call it sequential action.

(2) Embedding an SVG image in a node is possible, but if that SVG also contains an image, the browser won't see it. Besides that technical problem, there is also an epistemological argument not to do so. Between different scientific disciplines there is always an unruly zone where rules and terminology are incompatible. For example, while redundancy is seen as positive in ecology, redundancy in logic and information theory are to avoid. Ditto for metereology and climate science, between biology and sociology, and so on. There is also absolutely no intention to abolish the disciplines, but rather to cooperate across the boundaries of the disciplines.

In a node you can link to an explanatory text file (HTML or XML) in which you can embed an EDAG graph. The advantage of that solution is that you can make clear what the connection is between the two logical layers and where the boundaries are for each logical layer. You wil find an example of such an imbedding in the upper node of this EDAG.

(3) Different approaches are also related to time scales of analysis. This applies not only across disciplines but also within disciplines themselves. A good indication of that time scale per graph is highly recommended. This may even be necessary per node as you can see in the example below.

(4) Graphs provide the basic schema of algorithms. They are therefore also an exercise in algorithmic thinking.

(*) DAG in EDAG does NOT mean Directed Acyclic Graph. EDAG can also be used for cyclic processes.

Consulted Resources

Berners-Lee, Tim, James Hendler, and Ora Lassila. The semantic Web. Scientific American, 284(5):34–43, May 2001.

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/>

Ladkin, Bernard (2018), Causal Analysis of Incidents with Why-Because Analysis using the SERAS® , Software Toolkit, CAUSALIS Ingenieurgesellschaft mbH, 2008, revised 2018-02-14, <https://rvs-bi.de/research/WBA/WBA-NewIntro20180214.pdf>

Lewis, David, (2004). “Causation as Influence” (expanded version), in Collins, Hall, and Paul 2004, 75–106, <https://www.andrewmbailey.com/dkl/Causation_As_Influence_long.pdf>

Menzies, Peter, (2019), Counterfactual Theories of Causation, 29 October 2019, Stanford Encyclopedia of Pholosophy, <https://plato.stanford.edu/entries/causation-counterfactual/>

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>

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>

Schürmann, Tim, (WBA) 'Counterfactual Test’, Workgroup RVS, Faculty of Technology, Bielefeld University) <https://rvs-bi.de/research/WBA/IntroWBA-ENG.pdf>

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 >

van Benthem, Johan, (IEP), Modal Logic: A Contemporary View, University of Amsterdam, Stanford University, and Tsinghua University, The Netherlands, U. S. A., and China, <https://iep.utm.edu/modal-lo/>

Wielemaker, J. (2005). An Optimised Semantic Web Query Language Implementation in Prolog. In: Gabbrielli, M., Gupta, G. (eds) Logic Programming. ICLP 2005. Lecture Notes in Computer Science, vol 3668. Springer, Berlin, Heidelberg. <https://doi.org/10.1007/11562931_12>