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

Origins Basic Measures
Intro to the GIS&T Body of Knowledge First & Second Laws of Geography
Public Sector Origins Shape
Private Sector Origins Distance Operations
Academic Developments of GIS&T Directional Operations
Cognitive Areal Operations
Perceptions and Cognition of Geographic Phenomena Proximity & Distance Decay
Foundational Ontologies Adjacency and Connectivity
Ontologies for Analysis & Formation of Geospatial Concepts Resolution
Place and Landscape Spatial Autocorrelation
The Power of Maps and Mapping Geometric Primitives and Algorithms
Semantic Information Elicitation 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  
Properties Uncertainty
Networks Defined Problems of Scale and Zoning
Events and Processes Thematic Accuracy and Assessment
Neighborhoods Conceptual Models of Error and Uncertainty
Philosophical  
Philosophical Perspectives  
Epistemology  
Openness  

 

FC-30 - Private sector origins
  • Identify some of the key commercial activities that provided an impetus for the development of GIS&T
  • Differentiate the dominant industries using geospatial technologies during the 1980s, 1990s, and 2000s
  • Describe the contributions of McHarg and other practitioners in developing geographic analysis methods later incorporated into GIS
  • Evaluate the correspondence between advances in hardware and operating system technology and changes in GIS software
  • Describe the influence of evolving computer hardware and of private sector hardware firms such as IBM on the emerging GIS software industry
  • Discuss the emergence of the GIS software industry in terms of technology evolution and markets served by firms such as ESRI, Intergraph, and ERDAS
FC-26 - Problems of Scale and Zoning

Spatial data are often encoded within a set of spatial units that exhaustively partition a region, where individual level data are aggregated, or continuous data are summarized, over a set of spatial units. Such is the case with census data aggregated to enumeration units for public dissemination. Partitioning schemes can vary by scale, where one partitioning scheme spatially nests within another, or by zoning, where two partitioning schemes have the same number of units but the unit shapes and boundaries differ. The Modifiable Areal Unit Problem (MAUP) refers to the fact the nature of spatial partitioning can affect the interpretation and results of visualization and statistical analysis. Generally, coarser scales of data aggregation tend to have stronger observed statistical associations among variables. The ecological fallacy refers to the assumption that an individual has the same attributes as the aggregate group to which it belongs. Combining spatial data with different partitioning schemes to facilitate analysis is often problematic. Areal interpolation may be used to estimate data over small areas or ecological inference may be used to infer individual behaviors from aggregate data. Researchers may also perform analyses at multiple scales as a point of comparison.

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

Relationships between space and time evoke fundamental questions in the sciences and humanities. Many disciplines, including GIScience, consider that space and time extend in separate dimensions, are interchangeable, and form co-equal parts of a larger thing called space-time.  Our perception of how time operates in relation to space or vice verso influences how we represent space, time, and their relationships in GIS. The chosen representation, furthermore, predisposes what questions we can ask and what approaches we can take for analysis and modeling. There are many ways to think about space, time, and their relationships in GIScience. This article synthesizes five broad categories: (1) Time is independent of space but relates to space by movement and change; (2) Time collaborates with space to probe relationships, explanations, and predictions; (3) Time is spatially constructed and contained; (4) Time and space are mutually inferable; and (5) Time and space are integrated and co-equal in the formation of flows, events, and processes. Concepts, constructs, or law-like statements arise in each of the categories as examples of how space, time, and their relationships help frame scientific inquiries in GIScience and beyond.

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

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