Ury diagram

An Ury diagram is an infographic that is used to represent legal positions on a collection of cases, especially to illuminate Rhetoric legal arguments that are based on the principle of Argumentum a fortiori. When used as an aid to understanding legal positions and arguments contained in the Talmud (the primary source of Jewish law and theology), they are also referred to as Talmud diagrams. The visual nature of Ury diagrams adds clarity and rhetorical force to legal arguments. 
An Ury diagram is a type of ordered truth table wherein the cells in the table represent specific cases, and shading in the cells indicate whether a certain law applies to that case. For one and two-dimensional Ury diagrams, the cells are ordered in such a way that there is more reason for the law in question to apply as you move to cells that are above or to the right of the initial cell. It follows that if a certain cell is shaded, that a fortiori the cells above and to the right of the initial cell are also shaded which represent cases where there is more reason for the law in question to apply. 
Every Ury diagram represents a unique legal opinion on a range of cases. By comparing two or more Ury diagrams, it is easy to compare differences in legal opinions over a range of cases. The diagrams can be one, two, or three-dimensional, with the one-dimensional and two-dimensional diagrams being the most commonly used and the easiest to create and read. Each dimension relates to the degree of presence of a single factor that influences whether a certain law applies. Higher dimensional diagrams are used to represent situations where more than two factors exist.
Ury diagrams were developed as an aid to understanding and following arguments presented in the Talmud that are based on Talmudical hermeneutics, and in particular arguments that implicitly or explicitly rely on the Kal vachomer (Argumentum a fortiori). Authorities in the Talmud will often rule on a range of cases as part of a single opinion. Understanding where two authorities agree and where they differ is key to following the questions and responses contained within a particular passage. Opinions among later generations of authorities often differ as to what the earlier authorities actually held, adding further complexity to understanding the Talmud. This leads to a proliferation of cases and opinions which must be tracked by the student seeking to comprehend the legal discussion being presented. Ury diagrams are simple visual representations of complex opinions that summarize data in a compact space. Ury diagrams were first described in 2011
A simple example of a 2x2 Ury Diagram which indicates that the Law applies when B is present independent of whether A is present or not.
The Shading Rule applied repeatedly to a 2D Ury Diagram.
Ury diagrams are Table (information) that can have any dimension, but most commonly are of one or two dimensions, and less commonly of three dimensions. The cells, often simply called boxes or squares, each represent a specific case. The shading within a box indicates what the law is for that particular case. The meaning of each type of shading is defined by the Key which associates each type of shading with a particular Law. Any box that is shaded implies that the Law that is associated with that shading applies to the case corresponding to that box. Taken together, the shading within the collection of boxes is an expression of a legal opinion. Shading can consist of a color fill or a series of lines, with the latter being the easiest to construct using pencil and paper. A box that is left blank is also part of the legal opinion because it indicates that the Law or Laws listed in the Key do not apply to that case.
The columns and rows of an Ury diagram are arranged such that as you move in one direction, there is either more or less reason for the law to apply. In two dimensions the convention is that there is more reason for the law to apply as you move up a row or to the right among columns. As a result, there are more shaded boxes in the vicinity of the right upper corner of an Ury diagram than in other parts of the diagram. This ordering of the rows and columns allows inferences to be drawn from existing rulings to argue how new cases should be treated. Ordering the rows and columns in order of increasing reason allows the application of the principle of a fortiori to argue how other cases should be treated. 
==== The Shading Rule ====
As mentioned above, the rows and columns of an Ury diagram are arranged to make it easy to apply the principle of a fortiori to extend the law from cases where the law is known to cases where the law is not yet known. The rule by which this extension is expressed in an Ury diagram is known as the Shading Rule. For the common case of a two-dimensional Ury diagram where there is one shading type, the Shading Rule can be expressed as follows:
"If a box is shaded, all boxes above it and to its right are also shaded. If a box is blank, all boxes below it and to its left are also blank."
The Shading Rule is merely a statement of the fact that if a Law applies to a particular case, it also applies to a case where it has more reason to apply. If a Law does not apply to a particular case, it also does not apply to a case where it has less reason to apply. The figure to the right illustrates this point for a 3x3 2D Ury diagram. Starting with the first of the three Ury diagrams, it can be seen that the law is initially known for two of the nine cases. The box at the center of the Ury diagram is shaded, indicating that the Law applies to that case. The box to its immediate left is blank, indicating that the Law does not apply to that case. Applying the Shading Rule to the box at the center dictates that two boxes, one above it and one to its right should also be shaded. Applying the Shading Rule to either of the newly shaded boxes implies that the box at the top right corner should also be shaded. The Shading Rule can also be applied to the initially blank box, leading to the conclusion that the box below it should also be blank. The third of the three Ury diagrams show the result of this repeated application of the Shading Rule. Starting with two cases for which the law is known, the law for four additional cases has been determined using the Shading Rule which is just the visual equivalent of applying the principle of a fortiori. Of the nine possible cases, two are known initially, four are determined by the Shading Rule, but three remain indeterminate.
== Example ==
As an example of the application of an Ury diagram consider the following hypothetical case of a driver traveling at 50 mph (miles per hour) under rainy conditions who is pulled over by a police officer for speeding. The posted speed limit is 55 mph but the officer cites the driver for speeding in consideration of the weather at that time. The driver decides to challenge the citation in court and uses a series of three Ury diagrams to prove his case. The Ury diagrams are shown below in (a), (b) and (c). The Key below the diagrams tells us that shading indicates that the speed limit is exceeded and that a traffic violation has been committed. Normally, traffic citations are issued when the driver exceeds the speed limit by at least 5 mph. The rows are arranged in such a way that the higher up in rows, the more reason there is that there is a traffic violation. The columns are arranged in order of increasing speed; the farther one moves to the right, speed increases and there is more reason for one to be in violation of the law.
File:Ury Diagram Example - In a 55 mph zone, Ury Diagram (a) reflects the fact that a driver can be cited for driving 5 mph above the speed limit. For foggy conditions the speed limit is posted to be 35 mph as reflected in (b). In (c) the driver infers that the speed limit under rainy conditions is not 35 mph and should default to 55 mph. An alternative inference, eventually upheld by the judge, is that when it rains, it is true that the speed limit is not 35 mph but still may be as low as 40 or 45 mph.
Diagram (a) reflects the fact that exceeding the posted speed limit by 5 mph is considered "exceeding the speed limit" and can result in a citation. If a driver traveling at 60 mph in clear weather can be cited for speeding, then surely he or she can be cited for traveling at 60 mph when it is raining or foggy. This last conclusion follows from the principle of a fortiori or equivalently from the Shading Rule, namely that if the bottom right box in (a) is shaded, then certainly the boxes above it are shaded. An additional sign posting the speed limit is present and it states, "Maximum speed reduced to 35 mph in fog". That implies that a driver will be cited when driving 40 mph or more when fog is present. This additional restriction is indicated in (b) by shading the entire top row. In our example there is rain, which is represented by a row that lies between 'clear' and 'fog'. The posted signs are silent about the speed limit when it rains and so it is questionable what the speed limit is when it rains. This situation is expressed in (b) by the question marks that remain in the middle row. 
The driver argues that he can prove that he should not have been cited for driving 50 mph in the rain. According to the driver, as shown in (c), the sign reducing the speed limit to 35 mph in fog does not apply to rain and therefore the speed limit defaults to the usual 55 mph. Since he drove at 50 mph he clearly did not exceed the 55 mph speed limit and was incorrectly cited. The officer claims that she cited the driver because it was her determination that the maximum safe speed was at most 45 mph and she was correct for ticketing the driver for driving at 50 mph. Upon hearing both arguments, the judge upholds the citation based on the following argument. In addition to the posted signs, we must take into account the Assured clear distance ahead Law that states that a vehicle may not be driven at a speed that is unsafe for the existing conditions. It is true that we can infer from the sign that the speed limit in rain is not as low as 35 mph, as shown in (d) where the box corresponding to driving 40 mph in rain is not shaded. This does not rule out the possibility that the maximum safe speed in rain may be only 40 or 45 mph. The judge accepts the opinion of the officer that the maximum safe speed was at most 45 mph as shown in (d) and therefore finds the driver guilty of violating the Basic Speed Law and requires the driver to pay the amount indicated in the citation.
== Advantages ==
Ury diagrams are a form of data visualization for presenting legal opinions and legal arguments and therefore takes advantage of the human ability to process complex visual information and applies it to understanding legal logic. As seen in the example in the previous section, a single Ury diagram maps the law for nine different cases at the same time but is easily comprehended by the viewer. Each Ury diagram expresses a legal opinion and maps it to a pattern that can be easily understood and recalled. A series of Ury diagrams, as above, uses the technique of Small multiple to track the evolution of a legal argument in a way that it is easy to detect the cases in which two opinions differ. In the example above it is easy to see that the driver's opinion expressed in (c) and the officer's opinion expressed in (d) agree in eight cases but differ in the critical one case.