Topological Ontology and Logic of Qualitative quantity

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The link between Qualitative quantity and Topology (in particular Topological Data Analysis), and the proposition of the Qualitative quantity method as tool for the Topological Data Analisys, is encouraged by Richiro Mizoguchi’s interpretation offered in part “3. Quality and Quantity, 3.1 Background” from his “YAMATO : Yet Another More Advanced Top-level Ontology” – “e-Science needs data exchange world-wide. Especially, in biology and bio-informatics, data exchange has been intensively conducted through global collaboration in the daily activities. In order to make it smooth to exchange scientific data, the way of description must be compatible with each other. Description of data/objects is usually done by determining attribute values. However, quality description is not wellunderstood by practitioners. Even professionals seem not to agree on the common way of quality description of objects.” 38 According to Riichiro Mizoguchi, “There are at least three ways of quality description recommended by BFO, DOLCE and Galen(Alan 2010). BFO recommends (e.g., ) formalism, while DOLCE (e.g., ) and Galen (e.g., 5). The problem is two fold: (a) one way of representation is not enough for real world problems because there exist multiple kinds of quality descriptions in the real data and (b) there is no explicit model of how these three are different from and interrelated with each other. The ontology of Quality and Quantity in YAMATO tries to give fundamental conceptualization of those existing descriptions in one ontology. To do so, YAMATO distinguishes between quality in reality and quality description and has a type hierarchy which reflects existing notions used in quality descriptions.” Investigating “the underlying philosophy” of Quality, in part “3.2 Quality - 3.2.1 The underlying philosophy”, Riichiro Mizoguchi establishes that “one of the contributions of our ideas is clear distinction between attribute and attribute values. As far as I know, there are three dependent entities related to the term attribute: (1) attribute as a type that plays as dimension, (2) attribute as an instance and (3) attribute value that might correspond to quantity. However, some ontologies do not distinguish between (2) and (3). In this respect, DOLCE nicely differentiates instance of attribute from attribute value by introducing quality for attribute as an instance and quale/qualia for attribute value. This 38 Riichiro Mizoguchi, “YAMATO : Yet Another More Advanced Top-level Ontology”, pp.3-4: http://www.ei.sanken.osaka-u.ac.jp/hozo/onto_library/YAMATO101216.pdf 18
differentiation enables us to capture a thing, holding a quantity(qualia), that can change keeping its identity as we discuss it below. In other words, any quantity exist only one in the world independently of how many things have those quantities as their values. We build an ontology for each of attribute (generic quality) and attribute value(quantity) intended to describe things in terms of the combination of those dependent entities. We discuss each of the two in turn.” The figure above (marked as Fig.3 in Mizoguchi’s work) shows an example of quality. According to Mizoguchi, “the issue here is how to wisely model this quality. ..Fig. 3 also shows types and individuals underlying the quality. Among them, “John”, “160” and “cm” have no issue to discuss. Let us briefly investigate characteristics of the others. Firstly, “John’s height” is something associated with John and exists at the instance level. “Height” is generic in the sense that the entity which it is associated with is unspecified, but is more specific than “length” in the sense that it is dependent on what to measure and how. This suggests the notion of “quality role” played by length, which is an interesting topic, but it will be discussed later. The “length” is quite generic because it can be height, depth, distance, etc. according to the context and exists at the class level. Finally, “160cm long” seems to be quantity and exists at the instance level. In summary, issues include (1) if “160cm long” is a quality or a quantity, (2) if an instance of a quality is a quantity or not, (3) what is “John’s height”, (4) what is “height”, and (5) how is “length” different from “height” The following subsections are devoted to answer these questions.” Mizoguchi discusses the example of quality on change, illustrating with the “a boy named John who grows”, where the John’s height was 160cm in 2008 and 170cm in 2009. For Mizoguchi, “ontologically, in order to talk about change properly, we need a non-changing thing keeping its identity during the change process, otherwise, there cannot exist a change but just a difference. In the case of growing John, John and his height must keep their identities. That is, “John’s height” must have the same identity at the times of 2008 and 2009. The values, on the other hand, are 160cm in 2008 and 170cm in 2009, respectively, and they have their own different identity. This analysis reveals that “John’s height” has something having its identity and it is generic in the sense that its possible values are indefinite.” Later one Mizoguchi discusseses the “Quality role”: “We here discuss the notion of quality role. Many of the qualities people know are not basic quality (This term is temporary and will be renamed as generic quality type later.- Mizoguchi) but quality role. Let us take an example of height. It is a quality role whose basic quality is length. In the role theory (Mizoguchi 07), it can be said that “height role is played by length in the context of a human body”. Height is what is measured in the direction roughly along the vertical axis from the ground level to the top. Similarly, depth, width and distance are quality roles played by length as well. It is just like a man plays a husband role when he has got married and like a human plays a teacher role in the context of a school. Let us call quality such as length as basic quality temporarily. Examples of basic qualities include length, area, mass, temperature, flow rate, voltage, etc. Basic qualities are context-independent and intrinsically represent kinds of quality, and roughly equal to physical dimensions. Quality roles include height, depth, input flow rate, maximum weight, area of cross section, etc.“ 19
Page 1 and 2: Topological Ontology and Logic of Q
Page 3 and 4: agreements about the representation
Page 5 and 6: Science” (Wissenschaftslehre), Bo
Page 7 and 8: Leśniewski's student Alfred Tarski
Page 9 and 10: Mereotopology is a first-order theo
Page 11 and 12: only that between process and event
Page 13 and 14: hierarchies to represent their mutu
Page 15 and 16: meta attribute value counting_valu
Page 17: Fig. 2 Detail version of top-level
Page 21 and 22: 3.Quality: It is a property associa
Page 23 and 24: 3. The Topological Notion of Qualit
Page 25 and 26: series of Measure Relations” /b/,
Page 27 and 28: The true resurgence of Hegel’s Qu
Page 29 and 30: Kairos, Chora and Topos as follow:
Page 31 and 32: In Philosophical or Dialectical Her
Page 33 and 34: The roots of Hegel’s Qualitative
Page 35 and 36: Richter mentions these developments
Page 37 and 38: Name: Firstness. Secondness. Thirdn
Page 39 and 40: of something in its other. In his e
Page 41 and 42: This is not to say, however, that t
Page 43 and 44: One of the main concerns of hermene
Page 45 and 46: concept of spatiality. But they did
Page 47 and 48: David Gray Carlson’s “A Comment
Page 49 and 50: Hegel's great work on Logic, the
Page 51 and 52: For Paterson, the “true mathemati
Page 53 and 54: The term “social topology” is u
Page 55 and 56: of Leonard Euler and later with the
Page 57: To Meet the Other is to have the id

Topological Ontology and Logic of Qualitative quantity

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