Multivalued Logic

Problems with Classical Logic

Classic, two-valued logic is an important foundation in GIS for several reasons:

• All computer-based systems are based on the fundamental principle of logic, taking on truth values of 0 or 1 representing false and true, respectively. This is implemented as binary logic; turn-on/turn-off, blackand-white logic; and, ultimately, yes or no representations and decisions throughout the GIS workflow.
• The commonly implemented spatial analysis tools are driven by two-valued logic. It is implemented as Boolean algebra and is the basis of map algebra. Topology, spatial overlays, intersections, queries, and decision trees are all major GIS operations that use logical implications of two-valued logic.
• GIS tools utilizing the concept of probability and binary logic treat uncertainty and imprecision as a lack of truth that has to be eliminated as a major part of the traditional scientific method.
• Generally, in GIS, all information and knowledge are derived from data and facts that are seen to be either true or false.

The formal logic that has been used in science for over 2,000 years originated in the philosophical discussions of Plato and his student Aristotle, as well as among other ancient Greek mathematicians, logicians, and philosophers. Aristotle was among the first to propose formal logic as a tool for all other disciplines. Ever since logical calculus has existed, mathematicians and philosophers have tried to understand the meaning of truth. Throughout the centuries, different approaches toward formal logic have been developed, focusing either on formal issues or on epistemological problems.

Modern logic is closely related to scientific developments in the 19th and 20th century. George Boole, Gottlieb Frege, Bertrand Russell, and Ludwig Wittgenstein, among many others, were important for the development of modern mathematical and philosophical logic used in GIS and related disciplines. The history of modern logic was always inspired by the search for a perfect formal language, that is, to express all information and knowledge by an artificial, precise symbolic language that would eliminate all vagueness such as that found in natural languages, which are inherently vague and ambiguous.

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