As described before, there are many different methods available to represent medical knowledge; but one of the most excellent ones, meeting the needs for the special purposes of our medical decision-support system, is the knowledge representation method of MedFrame. An overall description of the knowledge representation framework of MedFrame is beyond the scope of this short introduction and can be found in detail in the other references. Therefore, the we rather intend to give a brief summary of basic knowledge representation entities in MedFrame/CADIAG-IV as necessary for understanding the knowledge acquisition framework that is described in this text.

1. Representation of Medical Concepts: In MedFrame/CADIAG-IV, a medical concept represents the top-most abstraction level of medical facts. The most important characteristic of a medical concept is that it is uniquely defined by a set of facets based on SNOMED international module concepts and a variable number of qualifiers; so all entities can be defined and identified in a stringent, coherent, and semantically meaningful way. Generally, two distinct subtypes of medical concepts are distinguished: First, the medical data class that represents measured quantitative data (e.g., results obtained from laboratory tests). Inherently, instances of medical data are numeric values and not applicable to the inference engine of MedFrame/CADIAG-IV unless converted into symbolic concepts. Second, the medical entity class that —in contrast with the medical data class— represents medical concepts on a symbolic level. Accordingly, instances of medical entities are applicable to the inference engine. For semantic reasons, it is distinguished three subtypes of medical entities: symptoms, diseases, and therapies.
   As stated above, a data-to-entity conversion has to be employed to transform numeric medical data into symbolic concepts to be usable in the inference process. To convert numeric medical data (e.g., ‘body temperature’) into symbolic ones (e.g. ‘body temperature, normal’ or ‘body temperature, raised’), we use a data-to-symbol conversion mechanism based on the concept of linguistic variables.
   For this purpose, it is defined a linguistic variable that denotes the observed medical data. The term set of this linguistic variable represents the interpretation categories of the respective medical data or, in other words, the set of symbolic concepts (symptoms) that a medical data can convert into. The numerical value of the medical data will be converted to the symbolic concept symptom by applying the membership function which defines the meaning of the symbolic concept to the numerical value. Hence, the concept of a linguistic variable, as it is used in the MedFrame framework, is used merely to define the term set as well as the meaning of the term set’s linguistic terms. The linguistic variable itself whose states are linguistic terms is not explicitly used. Now we are in the position to define a mapping between the Deutsch multi-layered structure of medical knowledge and the above terms as the following:
   ‘Observation’  -> ‘Medical data’
   ‘(Patho)physiological state’ -> ‘Symptom’
   ‘Disease state’ -> ‘Diagnosis’
   ‘Therapy’ -> ‘Therapy’
   One of the terms of the multi-layered structure is just left out: ‘Test’. This term is mapped to the ‘Examination’ type. An examination is the actual procedure to obtain patient’s state in means of observed medical data elements. This concept is explicitly represented because it is used to (a) establish a relationship between a medical data and the related symptom, (b) suggest further actions to the user —that means it is used to suggest specific procedures to obtain additional medical data elements—, and (c) treat with costs, invasiveness, and urgency information. Concerning the previous medical definitions, we are able to introduce several symbols and sets:
   O: the set of medical data items
   S: the set of all symptoms
   D: the set of all diagnoses
   T: the set of all therapies
   E: the set of all medical entities
   C: the set of all medical concepts
   According to the hierarchies of medical knowledge, we are able to establish the following subset hood relationship:
   
   This relationship is a good idea to logical representation of medical knowledge.
2. Representation of Relationships between Medical Concepts: A substantial portion of medical knowledge in MedFrame/CADIAG-IV’s knowledge base is represented by means of rules. In general, a rule consists of a left hand side (antecedent, premise), a conclusion operator, and a right hand side (consequent, conclusion). A smaller number of rules are concerned with taxonomic-hierarchical reasoning, medical data preprocessing and data-to-entity conversion, and meta-rules concerning the knowledge base. Here, the basic rules are discussed that denote associations between medical entities such as findings and diseases. This type of rules employs an implication operator that demands symbolic concepts as antecedents and consequents.
   In general, we distinguish rules that denote positive associations between antecedents and consequents from rules that denote negative associations. Both are characterized by a pair of fuzzy sets which in the case of a positive association are denoted as  “the frequency of occurrence of the antecedent with the consequent” and  “the strength of confirmation of the consequent by the antecedent”, and in the case of a negative association as  “frequency of occurrence of the antecedent with NOT the consequent” and  “the strength of exclusion of the consequent by the antecedent”.
   These fuzzy sets represent and qualify the vagueness and uncertainty of the relationships and are interpreted as fuzzy numbers. Actually, they are fuzzy numbers of the set . For the definition of their characterizing membership functions we use the function  hereafter.

   The rule base of MedFrame/CADIAG-IV, that is the total set of rules in the knowledge base, may be seen by fuzzy relations as follows:
   
   Please note that the above equation could either be an ordinary fuzzy relation or an L-fuzzy relation. A very important special kind of this equation is a type 2 fuzzy relation which describes the relationships between tuples of medical entities, positive or negative, as:
   
   Such binary fuzzy relations play a major rule in the fuzzy relation-based medical knowledge-based systems such as MedFrame\CADIAG-IV and are used to describe various relationships between medical entities.