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Schockaert, S. & De Cock, M. (2007). Reasoning about vague topological information. Proceedings of the ACM Conference on Information and Knowledge Management, 593-602. 

@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}
}

Author of the summary: Heather Burch, 2007, heather@burch.ca

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Natural language often describes topological information in an imprecise manner, resulting in a need to be able to capture this vagueness. Boundaries between neighbourhoods, such as “downtown Lisbon”, are often ill-defined. Fuzzy sets are often used to represent vague regions. Whether or not a certain places falls into a particular area is, therefore, a matter of degree. Schockaert has a diagram showing an example of a 3-dimensional representation of a relationship between two neighbourhoods. Modeling the fuzzy relationships between pairs of geographic features can take the form p and q are within walking distance to degree 0.6, to use an example from the paper.

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 to a degree, necessitating fuzzy reasoning to obtain a more cognitively adequate framework. For example, if one read in a natural language text that A was adjacent to B, then by the RCC-8 calculus definitions, one can conclude that both DC(A,B) and EC(A,B) are correct. However, one wants, based on the meaning of “adjacent” to say that only EC is correct. The solution that this paper use is that DC(A,B) is correct if the two places are disconnected and not close and EC(A,B) is correct if they are touching or close to each other. Closeness is a vague feature. This means that even if the two regions are themselves crisp, then the relations between them can still be vague.

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 (a1, a2) and (b1, b2) can be represented as the relationships between a1 and b1, a1 and b2, a2 and b1, and a2 and b2. Others argue that fuzzy set theory better captures topological information.

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.

Summary author's notes:

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