**3.1 Concepts**

196 Semantics – Advances in Theories and Mathematical Models

Fig. 2. Representation Language of Quality Indications and their values.

indicator is calculated to be the result of the algorithm, queries and data above.

In this chapter, we focus on the representation system of quality indicators.

for a given set of hospital stays.

**3. Medical service ontology** 

concepts.

respectively.

graph that expresses a set of hospital stays of patients who had operations for stomach cancers and a quantifying concept that calculate the average of length of the hospital stays

In a coherent manner, concepts and properties in MSO are translated to tables or columns in them in GDM. Also an objective graph is translated to a query on GDM through a mathematical interpretation defined in Section 5. Moreover, by mappings between GDM and data models of local medical databases, tables and queries on GDM are translated to those in the local medical databases. On the other hand, a quantifying concept is translated to an algorithm to enumerate tuples of the tables that are obtained to be the results of the tables and queries above and/or to calculate data of them. Finally, the value of a quality

In the sections from now, we define the three main components of the representation system of quality indicators: medical service ontology (MSO), objective graphs, and quantifying

MSO is an ontology consisting of concepts related to medical services. In this section, we define the ontology by defining its concepts and properties1. The ontology has been

1 In ontology engineering, concepts and properties in an ontology are often called classes and roles,

We first define concepts in the medical service ontology. Concepts in MSO are used as vocabularies to describe quality indicators. Many quality indicators are described as the number, the rate or the average of (a) set(s) of patients or events in hospitals that are in a state. Moreover, many patients, events and states (of patients) can be characterized by them. Thus, concepts of stakeholders (especially, patients), events and states (of patients) are particularly important.

We introduce main concepts in MSO, as follows. Because of space limitations, we define some main concepts only. We describe a concept by the [name of a concept]. The concepts below are indicated by brackets.


[number of years], [number of months],[number of weeks], [number of days]

A concept can be regarded as a set of instances of a given concept. Thus, we often identify the concept [patient] with the set of instances of that patient.

Representation System for Quality Indicators by Ontology 199

Fig. 4. Concepts and their attributes of patients' states.

Fig. 5. Concepts and their attributes of events for patients.

explanation of the relations between patients and other events.

1. Relations of patients and events: The relations are defined between the [patient] and all event concepts. For example, the following relation denotes the relations between

⟨subject (of an event)⟩⊆ [patient]×[hospital stay]. Note that these relations share the same name "subject (of an event)". We omit the

We define the primary relations between concepts.

**3.2.2 Relations between concepts** 

patients and their hospital stays.
