A Study on Plausible Mereotopological Models

• Main Authors: Shih-hsun Chen, 陳世勳
• Other Authors: Hsing-chien Tsai
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/17487596790703577217

碩士 === 國立中正大學 === 哲學所 === 98 === This paper is a note on treating “ROS (R3)” as a good way to describe regions. Ian Pratt-Hartmann (in [2]) has proposed this. In this paper, I will point out that there are two meanings to the term “mereotopology” as defined by Ian Pratt-Hartmann: a mereotopology as a structure of (1) a formal language of Boolean algebra, or (2) a first-order language that describes regions. Here we clarify the difference between the two, based on the difference in the existence of a region and that of a boundary. We can easily construct a Boolean algebraic structure CM (in this structure, a region contains its boundary) which is isomorphic to a given mereotopology M. However, although we also find that as a structure of first-order language, which describes regions, M is still batter than CM. Besides, we explain why Ian Pratt-Hartmann considers ROS(R3) (which is a mereotopology) to be a good way to describe regions. Moreover, we will supply some proofs which Ian Pratt-Hartmann omits.