A class is a category of items that share one or more common traits serving as criteria to identify the items belonging to the class.

An instance of a class is an item that has the traits that match the criteria of the intension of the class.

Interoperability means the capability of different information systems to communicate some of their contents. In particular, it may mean that

1. two systems can exchange information, and/or
2. multiple systems can be accessed with a single method.

The domain is the class for which a property is formally defined. This means that instances of the property are applicable to instances of its domain class. The range is the class that comprises all potential values of a property. That means that instances of the property can link only to instances of its range class.

Strict inheritance means that there are no exceptions to the inheritance of properties from superclasses to subclasses. For instance, some systems may declare that elephants are grey, and regard a white elephant as an exception. Under strict inheritance it would hold that: if all elephants were grey, then a white elephant could not be an elephant. Obviously not all elephants are grey. To be grey is not part of the intension of the concept elephant but an optional property. The CRM applies strict inheritance as a normalization principle.

Monotonic reasoning is a term from knowledge representation. A reasoning form is monotonic if an addition to the set of propositions making up the knowledge base never determines a decrement in the set of conclusions that may be derived from the knowledge base via inference rules. In practical terms, if experts enter subsequently correct statements to an information system, the system should not regard any results from those statements as invalid, when a new one is entered. The CRM is designed for monotonic reasoning and so enables conflict-free merging of huge stores of knowledge.

An instance of a property is a factual relation between an instance of the domain and an instance of the range of the property that matches the criteria of the intension of the property.

The difference between enduring and perduring entities is related to their behaviour in time. Endurants are wholly present (i.e., all their proper parts are present) at any time they are present. Perdurants, on the other hand, just extend in time by accumulating different temporal parts, so that, at any time they are present, they are only partially present, in the sense that some of their proper temporal parts (e.g., their previous or future phases) may be not present. Philosophers say that endurants are entities that are in time, while lacking however temporal parts (so to speak, all their parts flow with them in time). Perdurants, on the other hand, are entities that happen in time, and can have temporal parts (all their parts are fixed in time).” (Gangemi et al. 2002, pp. 166-181).

The extension of a class is the set of all real life instances belonging to the class that fulfil the criteria of its intension. This set is "open" in the sense that it is generally beyond our capabilities to know all instances of a class in the world and indeed that the future may bring new instances about at any time (Open World). An information system may at any point in time refer to some instances of a class, which form a subset of its extension.

The term primitive as used in knowledge representation characterizes a concept that is declared and its meaning is agreed upon, but that is not defined by a logical deduction from other concepts

Semantic interoperability means the capability of different information systems to communicate information consistent with the intended meaning. In more detail, the intended meaning encompasses 1. the data structure elements involved, 2. the terminology appearing as data and 3. the identifiers used in the data for factual items such as places, people, objects etc.

A property serves to define a relationship of a specific kind between two classes. The property is characterized by an intension, which is conveyed by a scope note. A property plays a role analogous to a grammatical verb, in that it must be defined with reference to both its domain and range, which are analogous to the subject and object in grammar (unlike classes, which can be defined independently). [...] Properties may themselves have properties that relate to other classes (This feature is used in this model only in order to describe dynamic subtyping of properties). Properties can also be specialized in the same manner as classes, resulting in IsA relationships between subproperties and their superproperties. In some contexts, the terms attribute, reference, link, role or slot are used synonymously with property.

The intension of a class or property is its intended meaning. It consists of one or more common traits shared by all instances of the class or property. These traits need not be explicitly formulated in logical terms, but may just be described in a text (here called a scope note) that refers to a conceptualisation common to domain experts. In particular the so-called primitive concepts, which make up most of the CRM, cannot be further reduced to other concepts by logical terms

The "Open World Assumption" is a term from knowledge base systems. It characterizes knowledge base systems that assume the information stored is incomplete relative to the universe of discourse they intend to describe. This incompleteness may be due to the inability of the maintainer to provide sufficient information or due to more fundamental problems of cognition in the system’s domain. Such problems are characteristic of cultural information systems. Our records about the past are necessarily incomplete. In addition, there may be items that cannot be clearly assigned to a given class. [...] In particular, absence of a certain property for an item described in the system does not mean that this item does not have this property. For example, if one item is described as Biological Object and another as Physical Object, this does not imply that the latter may not be a Biological Object as well. Therefore complements of a class with respect to a superclass cannot be concluded in general from an information system using the Open World Assumption.

A subclass is a class that is a specialization of another class (its superclass). Specialization or the IsA relationship means that: 1. all instances of the subclass are also instances of its superclass, 2. the intension of the subclass extends the intension of its superclass, i.e. its traits are more restrictive than that of its superclass and 3. the subclass inherits the definition of all of the properties declared for its superclass without exceptions (strict inheritance), in addition to having none, one or more properties of its own.

The complement of a class A with respect to one of its superclasses B is the set of all instances of B that are not instances of A. Formally, it is the set-theoretic difference of the extension of B minus the extension of A. Compatible extensions of the CRM should not declare any class with the intension of them being the complement of one or more other classes. To do so will normally violate the desire to describe an Open World. For example, for all possible cases of human gender, male should not be declared as the complement of female or vice versa. What if someone is both or even of another kind?

Syntactic interoperability means that the information encoding of the involved systems and the access protocols are compatible, so that information can be processed as described above without error. However, this does not mean that each system processes the data in a manner consistent with the intended meaning. For example, one system may use a table called “Actor” and another one called “Agent”. With syntactic interoperability, data from both tables may only be retrieved as distinct, even though they may have exactly the same meaning. To overcome this situation, semantic interoperability has to be added.

We use the term property quantifiers for the declaration of the allowed number of instances of a certain property that an instance of its range or domain may have. These declarations are ontological, i.e. they refer to the nature of the real world described and not to our current knowledge. For example, each person has exactly one father, but collected knowledge may refer to none, one or many.