O Level Notes : Geography - Geographic Information Systems - Boolean Logic & Overlays

This topic looks at what the Boolean logic is all about and how overlays are used in analysing data.

BOOLEAN LOGIC

Logic is reasoning according to set principles of validity. Computers use logic to perform certain tasks. This is why computers may not perform certain tasks which are not within their specified rules or principles. The software in computers work logically. Boolean logic is named after the mathematician George Boole.  This Boolean logic is a form of Algebra where letters and symbols are used to represent numbers and values in equations. The equations are then reduced to give True or False conclusions. 

GIS uses the Boolean logic to perform operations on attributes of Geographic features. Boolean logic is useful in both vector and raster systems. This Boolean logic use logical operations which are: AND, OR, XOR, and NOT. These operations can be used to analyse statements logically to decide whether the statements are True or False. For example, the statement that it is raining and it is during the day can only be true or false. Being day can only be true when it is in actual fact day and the same applies to being night. Using AND, OR, NOT and XOR, other True or False statements can be formed and presented using Truth tables.

Statement D says it is day time

Statement R says it is raining

The AND operator

The AND operator is the intersection of two sets. It considers those entities in a data set which belong to both sets of data. According to AND operator, it is False(F) when D and R are false, when D is F and R is T, when D is T and R is F but it is True(T) when we have both D and R being True. The true statement according to the AND operator is that it is raining and at the same time it is daytime. That will be the intersection of the two statements.

The OR operator

True or False Table for the OR operator

The OR operator is the union of the two sets of data. In this case the True statements will be whatever is True with any one of the two cases. If D or R is false when both D and R are false (it's not day time and it's not raining). It means none of the cases are contained in any of the two sets. This operator considers all of D and all of R.

The NOT operator

 The NOT operator

This operator shows entities which do not belong to one set but belongs to another. According to this operator, if it is False that it is not daytime then it is True that it is not D (day time) but if it is True that it is indeed day time then that it is NOT D (daytime) will be False.

The XOR Operator

 The XOR Operator

D        R    D X OR R

When D is true and R is true,  the combined expression (D OR R) is also true. The EOR or XOR is called the exclusive OR which is shown  above.

Venn diagram are useful in illustrating the Boolean logic in data interpretation. Taking for instance the 4 operators which have identified (AND, OR, XOR and NOT). The Boolean logic is portrayed visually using Venn diagram. Venn diagrams are useful in showing relationships between entities that can be grouped into specific groups or sets.

Boolean logic and Venn diagrams 

Venn diagrams are useful in illustrating the Boolean logic in data interpretation, taking for instance, the 4 operators which we have identified (AND, OR, XOR, NOT). The Boolean logic is portrayed visually using Venn diagram. Venn diagrams are useful in showing relationships between entities that can be grouped as specific groups or sets.

TheAND, OR, XOR and NOT operators are shown by Venn Diagrams.

TheAND Operator

The AND operator is the intersection of 2 sets. These 2 sets represent entities belonging to a certain group according to given attributes. The AND operator considers those entities in a data set, which belongs to both sets. These sets can be called Aand B. Fig 4.1 shows a Venn representation of the AND operator.

 The AND operator as Venn Diagram

The shaded part represent those entities found in both set A and B. Let us assume

that set A represents all agricultural activities near a city and B is market gardening. The shaded part represents all areas that are under market gardening and being near the city.   Some market gardens are not near the city due to improved transportation and refrigeration. These market gardens which are away from the city are represented by the unshaded part of set B. Not all agricultural activities near the city are market gardens. Dairy farms and many others are also found near the city. The unshaded part of set A represents agricultural activities near the city other than market gardening.

The OR Operator

The OR operation is the UNION of the 2 sets. They belong to both set A and Set B. In the example of farming activities near the city being set A and market gardening near the city being set B, the OR operator is shown by Venn diagrams completely shaded.

 The OR Operator as Venn

The NOT Operator

This is the difference operator. It is helpful in identifying the entities that belong to one but not to the other.

To illustrate the NOT Operator presented, let us say set A consists of all wildlife which are bovid and set B consists of all livestock. Some livestock are bovid, for example, goats and sheep. Boolean operations  show all of set A and part of set B joining. The shaded area shows all wildlife that is not bovid. These are not shared with set B for livestock. Livestock are not wildlife hence it representsANOT B.

The NOT Operator

Relational and conditional statements

Overlays involve making multiple input of layers. Maps are put together enabling GIS users to make important analysis. Relational statements in a GIS compares values and determines the relationship between them. Conditional statements are also made possible with GIS. Conditional statements enable GIS users to choose one option if the statement is true and another if it is false.

 OVERLAYS

An overlay is a GIS operation in which layers are joined so that integrated analysis of spatial and attribute data is made possible. By now you should know which layers are in GIS. Layers are also called themes and overlays lay these themes together. Overlaying creates composite maps which enable relationships amongst features to be identified. Most GIS softwares have tools which enable overlaying of both vector and raster data. This entails joining two or more vector or raster data. A good example of an overlay function is laying a road map on the cities and towns in a country. The final composite map made will show roads linking cities and towns. This enables distances between cities or towns to be calculated. Connectedness of cities and towns is shown. More sophisticated operations can also be performed, such as multiplying and adding map attributes for different value to determine averages and co-occurrences.

 OVERLAYAPPROACHES Region wide overlay

It is also called the "cookie cutter approach". Through this approach, overlay analysis allow natural features, that is forests, boundaries or soil polygons to become the spatial area(s) which are analysed on another map.

Region Wide Overlay

The layer for slope is overlain with the layer for patches of forests. The resultant map shows how the forest patches are distributed on the slope. The relationship between slope and forests is shown. Analysis as to why certain parts of the slope do not have patches of forest can be made. 

Topological Overlay

Maps are overlain to show features occurring at the same location. This is done by putting different maps on top of another using GIS and then finding all new intersecting lines. The new points where lines come together are set at these new intersections. Finally, the topographic structure of the data is rebuild and the multifactorial attributes are attached to the new area features. 

Neighbourhood Function

Neighbourhood function is useful in showing relationships between one object and other surrounding objects. This function is useful for development planners as it shows land uses which are next to each other. In urban planning it helps planners to locate facilities such as sewage works, dumping sites and others in relation to certain facilities such as water sources and residential areas.

VECTOR OVERLAYS

Vector data is joined to give a more complex theme. Vectors are points, lines and polygon features. Overlaying vector works on 3 processing algorithms. These are:

• Point- in- polygon
• Line- in- polygon
• Polygon- on- polygon

The Boolean operators (AND, OR, XOR and NOT) identified in the previous units are used in these overlays. When the layers are laid one on top of another, Boolean logical operations are used to determine which part of a layer is another, CONTAINED AND NOT CONTAINED within another layer in the system. There are numerous vector overlay operations and they come in basic operations of UNION, INTERSECTION, INCLUDE and EXCLUDE.

UNION

This operation is the same as the Boolean logical operator OR. This means that all input layers will be present in the output layer. All the elements of the first map (input coverage) and the second map (union coverage) are contained in the final map (output coverage map).

 Union Overlays

Let us assume that map 1 shows all Zimbabwe's farming regions and map 2 shows soil types. Creating an overlay of the two maps will result in a map showing all the farming regions and the types of soil. We can be able to see which regions have better soils. We can even add another layer of temperature or rainfall and the Union(OR) operator will enable us to see the relationships clearly.

INTERSECTION

This is the equivalent of the Boolean logic operator AND. In this case the elements of both input layers that coincide in the same geographic extension will be part of the final output layer.

 Intersection Overlays

INCLUDED (CONTAINED)

The output of the overlay contains all the elements present in the first input layer plus all elements present in the same geographic extension of the second input layer. For instance, to create a new layer which we will refer to as Map 3 containing 2 maps; hydrological network (map 2) and the land cover (map 1). When the two maps are joined in an overlay using the included operation they give a new map showing a combination of rivers and land cover.

EXCLUDE (NOT CONTAINED)

The output of the overlay in this case contain the elements of the first input layer that do not match with the geographical extent of the second input layer. For example, to create a new layer (Map 3) containing agricultural areas (Map 1) which are located far away from the noisy roads (Map 2), the overlay will contain elements on agriculture areas far away from noisy areas. Those near noisy roads are not shown.

With these Boolean logic operations, spatial analysis are made more meaningful.

Boolean logic and overlays provide the following advantages:

• They enable comparisons to be made between phenomena.
• They enable us to determine whether a particular condition is false or true.
• They enable the computing of new attributes in topographical overlays.
• The use of Venn diagrams gives a clear pictorial impression.
• They show relationships between features.

Here is what we discussed in this topic

• Boolean logic is portrayed visually in the form of Venn diagrams.
• Venn diagrams can take any shape.
• Overlays join different themes to be able to identify relationships.
• Boolean logic uses the operator AND, OR, X OR and NOT to see whether a particular condition is true or false.
• Region Wide overlay analysis allows natural features such as forests, boundaries or soil types to become spatial areas that are analysed on another map.

• Neighbourhood function analyses the relationship between an object and similar objects.

• Both vector and raster can have overlays.

Definition of terms used in this topic

Overlays: these are GIS operations which join sets of data or themes to identify relationships.

Venn  Diagrams:  these  are  diagrammatic  illustrations  of  Boolean  logic operations.

Neighbourhood function: is an overlay function which show relationships between one object and other surrounding objects.

GIS: Geographic Information Systems. Is a computerised system that enables

users to process, analyse, interpret and present spatial data.