Foundational Concepts

The foundational concepts are the elementary building blocks and context setting constraints of all other entries in the BoK. The latter encompass the philosophical and mathematical support for GIScience as well as data models, while the constituent elements include, among others, notions of scale, spatial data quality, and openness. This knowledge area is also the place to look for the origins and future of GIScience.

Topics in this Knowledge Area are listed thematically below. Existing topics are in regular font and linked directly to their original entries (published in 2006; these contain only Learning Objectives). Entries that have been expanded and revised are in bold. Forthcoming, future topics are italicized

Philosophical Basic Measures
Metaphysics and Ontology Distance, Length, and Direction
Epistemology Shape
Philosophical Perspectives Area and Region
Cognitive Proximity & Distance Decay
Perceptions and Cognition of Geographic Phenomena Adjacency and Connectivity
From Concepts to Data Resolution
Place and Landscape Geometric Primitives
The Power of Maps Spatial Autocorrelation
Learning from Experience Interrogating Geographic Information
Domains of Geographic Information Set Theory
Space Structured Query Language (SQL) and Attribute Queries
Time Spatial Queries
Relationships between Space and Time Uncertainty
Properties Error
Networks Defined Problems of Scale and Zoning
Scale and Generalization Thematic Accuracy
Events and Processes Definitions within a Conceptual Model of Uncertainty
Origins Social
Public Sector Origins  Openness
Private Sector Origins  
Academic Origins  

 

FC-10 - Properties
  • Formalize attribute values and domains in terms of set theory
  • Develop alternative forms of representations for situations in which attributes do not adequately capture meaning
  • Define Stevens’ four levels of measurement (i.e., nominal, ordinal, interval, ratio)
  • Describe particular geographic phenomena in terms of attributes
  • Determine the proper uses of attributes based on their domains
  • Characterize the domains of attributes in a GIS, including continuous and discrete, qualitative and quantitative, absolute and relative
  • Recognize situations and phenomena in the landscape which cannot be adequately represented by formal attributes, such as aesthetics
  • Compare and contrast the theory that properties are fundamental (and objects are human simplifications of patterns thereof) with the theory that objects are fundamental (and properties are attributes thereof)
  • Recognize attribute domains that do not fit well into Stevens’ four levels of measurement such as cycles, indexes, and hierarchies
FC-17 - Proximity and distance decay
  • Describe real world applications where distance decay is an appropriate representation of the strength of spatial relationships (e.g., shopping behavior, property values)
  • Explain the rationale for using different forms of distance decay functions
  • Explain how a semi-variogram describes the distance decay in dependence between data values
  • Outline the geometry implicit in classical “gravity” models of distance decay
  • Plot typical forms for distance decay functions
  • Write typical forms for distance decay functions
  • Write a program to create a matrix of pair-wise distances among a set of points
  • Describe real world applications where distance decay would not be an appropriate representation of the strength of spatial relationships (e.g., distance education, commuting, telecommunications)
FC-29 - Public sector origins
  • Identify some of the key federal agencies and programs that provided the impetus for the development of GIS&T
  • Explain how the federalization of land management in Canada led to the development of the Canadian Geographic Information System in the 1960s
  • Discuss the role of the U.S. Census Bureau in contributing to the development of the U.S. geospatial industry
  • Discuss the role of the U.S. Geological Survey in contributing to the development of the U.S. geospatial industry
  • Describe the mechanical and computerized technologies used by civilian and military mapping agencies between World War II and the advent of GIS
  • Trace the history of the relationship between the intelligence community and the geospatial industry
  • Compare and contrast the initiatives of various countries to move their national mapping activities to geospatial data
  • Describe the role of NASA and the Landsat program in promoting development of digital image processing and raster GIS systems
FC-09 - Relationships between space and time
  • Discuss common prepositions and adjectives (in any particular language) that signify either spatial or temporal relations but are used for both kinds, such as “after” or “longer”
  • Describe different types of movement and change
  • Understand the physical notions of velocity and acceleration which are fundamentally about movement across space through time
  • Identify various types of geographic interactions in space and time
  • Compare and contrast the characteristics of spatial and temporal dimensions
FC-21 - Resolution

Resolution in the spatial domain refers to the size of the smallest measurement unit observed or recorded for an object, such as pixels in a remote sensing image or line segments used to record a curve. Resolution, also called the measurement scale, is considered one of the four major dimensions of scale, along with the operational scale, observational scale, and cartographic scale. Like the broader concept of scale, resolution is a fundamental consideration in GIScience because it affects the reliability of a study and contributes to the uncertainties of the findings and conclusions. While resolution effects may never be eliminated, techniques such as fractals could be used to reveal the multi-resolution property of a phenomenon and help guide the selection of resolution level for a study.

FC-11 - Set Theory

Basic mathematical set theory is presented and illustrated with a few examples from GIS. The focus is on set theory first, with subsequent interpretation in some GIS contexts ranging from story maps to municipal planning to language use. The breadth of interpretation represents not only the foundational universality of set theory within the broad realm of GIS but is also reflective of set theory's fundamental role in mathematics and its numerous applications. Beyond the conventional, the reader is taken to see glimpses of set theory not commonly experienced in the world of GIS and asked to imagine where else they might apply. Initial broad exposure leaves room for the mind to grow into deep and rich fields flung far across the globe of academia. Direction toward such paths is offered within the text and in additional resources, all designed to broaden the horizons of the open-minded reader.

FC-15 - Shape

Shape is important in GI Science because the shape of a geographical entity can have far-reaching effects on significant characteristics of that entity. In geography we are mainly concerned with two-dimensional shapes such as the outlines of islands, lakes, and administrative areas, but three-dimensional shapes may become important, for example in the treatment of landforms. Since the attribute of shape has infinitely many degrees of freedom, there can be no single numerical measure such that closely similar shapes are assigned close numerical values. Therefore different shape descriptors have been proposed for different purposes. Although it is generally desirable for a shape descriptor to be scale invariant and rotation invariant, not all proposed descriptors satisfy both these requirements. Some methods by which a shape is described using a single number are described, followed by a discussion of moment-based approaches. It is often useful to represent a complex shape by means of a surrogate shape of simpler form which facilitates storage, manipulation, and comparison between shapes; some examples of commonly used shape surrogates are presented. Another important task is to compare different shapes to determine how similar they are. The article concludes with a discussion of a number of such measures of similarity.

FC-07 - Space
  • Differentiate between absolute and relative descriptions of location
  • Define the four basic dimensions or shapes used to describe spatial objects (i.e., points, lines, regions, volumes)
  • Discuss the contributions that different perspectives on the nature of space bring to an understanding of geographic phenomenon
  • Justify the discrepancies between the nature of locations in the real world and representations thereof (e.g., towns as points)
  • Select appropriate spatial metaphors and models of phenomena to be represented in GIS
  • Develop methods for representing non-cartesian models of space in GIS
  • Discuss the advantages and disadvantages of the use of cartesian/metric space as a basis for GIS and related technologies
  • Differentiate between common-sense, Cartesian/metric, relational, relativistic, phenomenological, social constructivist, and other theories of the nature of space
FC-37 - Spatial Autocorrelation

The scientific term spatial autocorrelation describes Tobler’s first law of geography: everything is related to everything else, but nearby things are more related than distant things. Spatial autocorrelation has a:

  • past characterized by scientists’ non-verbal awareness of it, followed by its formalization;
  • present typified by its dissemination across numerous disciplines, its explication, its visualization, and its extension to non-normal data; and
  • an anticipated future in which it becomes a standard in data analytic computer software packages, as well as a routinely considered feature of space-time data and in spatial optimization practice.

Positive spatial autocorrelation constitutes the focal point of its past and present; one expectation is that negative spatial autocorrelation will become a focal point of its future.

FC-13 - Spatial queries
  • Demonstrate the syntactic structure of spatial and temporal operators in SQL
  • State questions that can be solved by selecting features based on location or spatial relationships
  • Construct a query statement to search for a specific spatial or temporal relationship
  • Construct a spatial query to extract all point objects that fall within a polygon
  • Compare and contrast attribute query and spatial query

Pages