Causal notation

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Causal notation is notation used to express cause and effect.

In nature and human societies, many phenomena have causal relationships where one phenomenon A (a cause) impacts another phenomenon B (an effect). Establishing causal relationships is the aim of many scientific studies across fields ranging from biology^[1] and physics^[2] to social sciences and economics.^[3] It is also a subject of accident analysis,^[4] and can be considered a prerequisite for effective policy making.

To describe causal relationships between phenomena, non-quantitative visual notations are common, such as arrows, e.g. in the nitrogen cycle or many chemistry^[5]^[6] and mathematics^[7] textbooks. Mathematical conventions are also used, such as plotting an independent variable on a horizontal axis and a dependent variable on a vertical axis,^[8] or the notation $y=f(x)$ to denote that a quantity " $y$ " is a dependent variable which is a function of an independent variable " $x$ ".^[9] Causal relationships are also described using quantitative mathematical expressions.^[10] (See Notations section.)

The following examples illustrate various types of causal relationships. These are followed by different notations used to represent causal relationships.

^ Marshall, BarryJ; Warren, J.Robin (June 1984). "Unidentified curved bacilli in the stomach of patients with gastritis and peptic ulceration". The Lancet. 323 (8390): 1311–1315. doi:10.1016/S0140-6736(84)91816-6. PMID 6145023. S2CID 10066001.
^ Aspect, Alain; Grangier, Philippe; Roger, Gérard (12 July 1982). "Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment : A New Violation of Bell's Inequalities". Physical Review Letters. 49 (2): 91–94. Bibcode:1982PhRvL..49...91A. doi:10.1103/PhysRevLett.49.91.
^ Fischer, Stanley; Easterly, William (1990). "The economics of the government budget constraint". The World Bank Research Observer. 5 (2): 127–142. CiteSeerX 10.1.1.1009.4220. doi:10.1093/wbro/5.2.127.
^ Ladkin, Peter; Loer, Karsten (April 1998). Analysing Aviation Accidents Using WB-Analysis - an Application of Multimodal Reasoning (PDF). Spring Symposion. Association for the Advancement of Artificial Intelligence. Archived from the original (PDF) on 2022-12-21.
^ Bruice, Paula Yurkanis (2007). Organic chemistry (5th ed.). Pearson Prentice Hall Upper Saddle River, NJ. p. 44,45. ISBN 978-0-13-196316-0.
^ Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey; Madura, Jeffry D. (2007). General Chemistry Principles & Modern Applications (9th ed.). Pearson Prentice Hall Upper Saddle River, NJ. pp. 573–650. ISBN 978-0-13-149330-8.
^ B. George, George (2007). Thomas' calculus (11th ed.). Pearson. p. 20. ISBN 978-0-321-18558-7.
^ Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey; Madura, Jeffry D. (2007). General Chemistry Principles & Modern Applications (9th ed.). Pearson Prentice Hall Upper Saddle River, NJ. p. 575. ISBN 978-0-13-149330-8.
^ B. George, George (2007). Thomas' calculus (11th ed.). Pearson. p. 19. ISBN 978-0-321-18558-7.
^ Pearl, Judea; Mackenzie, Dana (2018-05-15). The Book of Why: The New Science of Cause and Effect. Basic Books. ISBN 9780465097616.

[Marshall1-1] Marshall, BarryJ; Warren, J.Robin (June 1984). "Unidentified curved bacilli in the stomach of patients with gastritis and peptic ulceration". The Lancet. 323 (8390): 1311–1315. doi:10.1016/S0140-6736(84)91816-6. PMID 6145023. S2CID 10066001.

[Aspect1-2] Aspect, Alain; Grangier, Philippe; Roger, Gérard (12 July 1982). "Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment : A New Violation of Bell's Inequalities". Physical Review Letters. 49 (2): 91–94. Bibcode:1982PhRvL..49...91A. doi:10.1103/PhysRevLett.49.91.

[Fischer1-3] Fischer, Stanley; Easterly, William (1990). "The economics of the government budget constraint". The World Bank Research Observer. 5 (2): 127–142. CiteSeerX 10.1.1.1009.4220. doi:10.1093/wbro/5.2.127.

[4] Ladkin, Peter; Loer, Karsten (April 1998). Analysing Aviation Accidents Using WB-Analysis - an Application of Multimodal Reasoning (PDF). Spring Symposion. Association for the Advancement of Artificial Intelligence. Archived from the original (PDF) on 2022-12-21.

[:4-5] Bruice, Paula Yurkanis (2007). Organic chemistry (5th ed.). Pearson Prentice Hall Upper Saddle River, NJ. p. 44,45. ISBN 978-0-13-196316-0.

[:5-6] Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey; Madura, Jeffry D. (2007). General Chemistry Principles & Modern Applications (9th ed.). Pearson Prentice Hall Upper Saddle River, NJ. pp. 573–650. ISBN 978-0-13-149330-8.

[:9-7] B. George, George (2007). Thomas' calculus (11th ed.). Pearson. p. 20. ISBN 978-0-321-18558-7.

[8] Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey; Madura, Jeffry D. (2007). General Chemistry Principles & Modern Applications (9th ed.). Pearson Prentice Hall Upper Saddle River, NJ. p. 575. ISBN 978-0-13-149330-8.

[9] B. George, George (2007). Thomas' calculus (11th ed.). Pearson. p. 19. ISBN 978-0-321-18558-7.

[:10-10] Pearl, Judea; Mackenzie, Dana (2018-05-15). The Book of Why: The New Science of Cause and Effect. Basic Books. ISBN 9780465097616.

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