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@InProceedings{SchockaertdeCock2007, author = {S. Schocaert and M. De Cock}, title = {Reasoning about vague topological information}, booktitle = {Proceedings of the ACM Conference on Information and Knowledge}, pages = {593-602}, year = {2007}, month = {November}, organization = {ACM} }

- Topological information as represented in a vague manner
- Using Region Connection Calculus to capture fuzzy relationships between pairs of topological regions

In RCC-8 (Region Connection Calculus) calculus, topological information is expressed as eight different types of relations. These are disconnected (DC, two circles that do not touch), partially overlapping (PO, two circles with some overlap), externally connected (EC, shown as two tangential circles), tangential proper part (TPP, one circle contained within another, touching the boundary of the outer circle), non-tangential proper part (NTPP, one circle within another, without touching the boundaries of the larger circle), TPP-1 (the inverse of TPP), NTPP-1 (the inverse of NTPP), and equals (EQ, two circles of the same size in the same place). These descriptions are suited to a range of applications, but fail to capture the vagueness of real-world topological information.

The vagueness in topological information stems from the vagueness of the regions involved. Regions can be thought to overlap

One manner of visualizing this relationship is to use “egg yolk calculus”. In egg yolk calculus, a vague region is represented by two circles, one its lower approximations, the other the higher. The result is a circle-within-a-circle that can be used to reason. Topological relations between (

Being able to extract topological information from natural language would be useful for many applications. However, natural language uses topological terms in a variety of ways that do not fit the rigid structure of RCC-8. Schockaert’s example uses a number of sentences describing the relationships between downtown Lisbon, Baixa, and Chiado. Each of the sentences describes a different relationship between the three regions. Although all the sentences were true, the resulting RCC results in inconsistency. Both EC(Baixa, Chiado) and DC(Baixa, Chiado) are found in web documents. However, all four can be found to be consistent if fuzzy reasoning is implemented, to say that each of the relationships is true to a degree.

The fuzzy truth calculus can also be used to handle entailment, best true value bound, and inconsistency repairing; as shown by the examples in section 5.4. The time complexity of these reasoning tasks is the same as their counterparts in plain RCC-8 calculus.

- Because of the difficulty typing the symbols for the equations given in this article, I have left out the math in this summary.

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