Where Is Central Ohio? Many-Valued Logic Approaches to Understanding and Measuring Vague Geographic Regions

Geographic regions are often vague or uncertain because they do not have clearly defined boundaries. The region referred to as Central Ohio, for example, is commonly recognized and referred to by people in the area around Columbus, Ohio. For places that are near Columbus, however, people are often indeterminate about whether they are in or out of the region. This article discusses the use of a suite of formal approaches known as many-valued logic in understanding and measuring the vagueness of regional terms such as Central Ohio. Instead of fixing places as being either in or out of the region, a many valued logic approach accepts other logic values such as indeterminate, both, and neither. An experiment was designed to ask people positive and negative questions about whether each one of sixty-seven selected Ohio cities was in or not in Central Ohio. We progressively analyze the experimental data, starting with a three-valued logic approach to identifying cities that are indeterminate when interviewees try to decide if they are in Central Ohio. Then four- and six-valued logic approaches are developed to further measure the indeterminacy. Finally, a fuzzy logic approach is used to quantify the degree of truth of any given location with respect to being in Central Ohio. Our results show that these formal approaches can be used to effectively unveil the characteristics of vague regional concepts. We also demonstrate how fuzzy logic can be used to conduct analysis such as estimating the population in a vague geographic region.