Topological Ontology and Logic of Qualitative quantity

only that between process and event but also that between a pulse and a sequence of pulses
and that between to grow and to cut, etc.”
The three theories of YAMATO are on:
• (1) Quality and quantity
• (2) Representations(content-bearing things)
• (3) Objects, processes and events
According to Riichiro Mizoguchi “careful examination of them (the well-known “upper
ontologies”) reveals some room for improvement in three respects: (1) Quality and quantity,
(2) Ontology of representation, and (3) Distinction between processes and events.” 33 As
Mizoguchi establishes “… quality and quantity need more careful investigation. One of the
most sophisticated property ontologies is found in DOLCE. It specifies value space for each
quality type under the name of Quality space(region). A remarkable feature of DOLCE’s
conceptualization about it is the clear distinction between the quality an object possesses
and the quality value(quale/qualia) itself.”
For Mizoguchi “no existing upper ontology distinguishes between quality in reality and
quality description, which causes some confusion when talking about quality and quantity.”
Mizoguchi believes that “quality ontology should contribute to facilitation of data
interoperability as well as capturing quality ontologically.”
The topological notion of quality and quantity is evident in the understanding and definition
of “quality” in ontology YAMATO. The definition of quality follows the threefold of concept
in YAMATO - “basic concepts”, “role”, and “role holder”. Quality is dependent attribute of
the basic concept, which preserved its identity unchanged during the occurrence of
changes of its meaning with the time flow. Topology is concerned with properties or
qualities that are preserved under continuous deformations of objects. The topological
notion of quality and quantity in this ontology is demonstrated by the simultaneous of these
two processes, first by the preservation of identity and second by the contiuous change of
the meaning.
In YAMATO the notion of quality is divided in quality role and in quality role type. Richiro
Mizoguchi illustrate this notions of quality with the example of the statement “John’s height
of 160 im long”. Here this division of quality role and quality role type is presented in the
parts of the statement, where John is the role holder (object/human), element John’s height
is the quality role (particul dependent attribute) of height associated with particular role
holder (John), and element height is the quality role type, not John’s hight but just the hight
(dependent on the way of measuring). After measuring the hight will be length (generic
quality type), in our example the length quantity is “160 cm long”, where “160” is number
and “cm” is unit/dimension.
33
http://www.ei.sanken.osaka-u.ac.jp/hozo/onto_library/YAMATO101216.pdf
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