The appendix contains an extended version of  2.3.2 Necessary Conditions and Sufficient Definitions supported by more detailed examples.


The stated view of concept definition consists of one or more assertions made by SNOMED CT authors

Necessary Conditions

Each time an assertion is made about a concept, an author must decide if that assertion is a necessary condition.  If the assertion is always true for that concept and its subtypes, it is a necessary condition.

  • This implies that for all instances of that concept or its subtypes, the assertion must be true, even if it has not been explicitly stated.

A necessary condition is defined as a characteristic that is always true of a concept.


Sufficient Definitions

For each concept an author must decide if there are one or more sets of assertions that form a sufficient definition of that concept. A set of assertions is a sufficient definition if it distinguishes a concept and its subtypes from other concepts. 

  • This implies that if all assertions in the set are true for a concept, it must be an instance of the defined concept or a subtype of that concept.

A sufficient definition is a set of characteristics which distinguish a concept and its subtypes from all other concepts


  • Any concept that matches the sufficient definition is equivalent to or a subtype of the defined concept.
  • concept may have more than one sufficient definition. In that case any concept that matches at least one of these sufficient definitions is equivalent to or a subtype of the defined concept.


Concepts with no Sufficient Definitions

concept that has no sufficient definitions is a primitive concept

Because primitive concepts have no sufficient definitions it is not possible for a description logic classifier to determine if other concepts are subtypes of this concept. Similarly, it is not possible to automatically determine whether an expression is a subtype of a primitive concept. Therefore, only concepts or expressions that explicitly state they are subtypes of primitive concepts will be treated as subtypes when applying expression constraints or undertaking analysis. 

However, note that this does not prevent a primitive concept being classified as a subtype of a sufficiently defined concept

Concepts with a Sufficient Definition

concept that has at least one sufficient definition is a sufficiently defined concept

description logic classifier can determine whether the stated definitions of other concepts meet at least one of the sufficient definitions and if so will classify these concepts as its subtypes. Similarly, it is possible to determine whether an expression is equivalent to or a subtype of a sufficiently defined concept. Therefore, where expression constraints or queries refer to sufficiently defined concepts the results will include the inferred subtypes of these concepts.

Sufficiently Defined Concepts with Necessary Conditions

If a sufficiently defined concept has one or more additional necessary conditions then any concept or expression that satisfies one of its sufficient definitions will also inherit any necessary conditions.

For example one sufficient definition of 397825006 | Gastric ulcer (disorder)| is an ulcer in a stomach structure:

However, another definition could be created with a more specific site gastric mucosa: In both cases these definition are equivalent to  397825006 | Gastric ulcer (disorder)| . The more general definition is flexible when it comes to allowing refinement to a specific location of the ulcer within the stomach, which is actually useful information. It also avoids requiring an expression to refer specifically to the mucosa (stomach lining), which is where all gastric ulcers occur.

For example, an expression including the specific location could look like this

This satisfies the sufficient definition because the finding site is a subtype of stomach structure. This will therefore classify as a type of  397825006 | Gastric ulcer (disorder)|  located in the anterior wall of the gastric fundus. The problem is that a query for disorders of the gastric mucosa will not find this expression. <<  64572001 |disease| 363698007 |finding site|  =  78653002 |gastric mucosa| However, adding the definition that refers to the gastric mucosa as an additional necessary condition can solve this problem. The expression satisfies the sufficient definition implying this is a type of  397825006 | Gastric ulcer (disorder)| . The fact that it is a type of gastric ulcer causes it to inherit  363698007 | finding site|  =  78653002 | gastric mucosa|  so it will now be included in the query for disease in the gastric mucosa.

A Definition that is Both Necessary and Sufficient

The definition shown in  Table D.2-1 provides an example of a simple case.

  • The === symbol indicates that the concept definition is equivalent to the concept. 
    • This means that each of the assertions in the definition is necessarily true for all instance of the concept  710785000 | Laparoscopic repair of hernia| .
    • It also means that this definition is sufficient, because if all the assertions are true, this implies this is either the concept or a subtype of the concept.

Table D.2-1: Stated view of the definition of |Laparoscopic repair of hernia|

A Definition that is Necessary but Not Sufficient

The definition shown in  Table D.2-2 provides an example of another simple case.

  • The <<< symbol indicates that the concept is a subtype of the concept definition. 

Table D.2-2: Stated view of the definition of |Acute benign pericarditis|

A Definition that is Sufficient with Assertions that are Not Necessarily True

This example illustrates a type of definition that was not supported prior to the enhancement to SNOMED CT support for advanced description logic. Therefore, the definition shown is for illustration only and will not be found in current releases of SNOMED.

The definition shown in  Table D.2-3 provides an example of a more complex case. 

Table D.2-3: Possible stated view of the definition of |Secondary diabetes mellitus|

Sufficiently Defined

  1. A sufficiently defined concept is concept with one or more sufficient definitions.



  2. Primitive

    A primitive concept is concept without a sufficient definition in the necessary normal form distributed in the relationship.



Necessary Conditions

All SNOMED CT defining relationships currently released are necessarily (always) true for the concept defined. Relationships that are necessarily true are also know as necessary conditions.

A necessary condition is defined as a characteristic that is always true of a concept.


Sufficient Sets of Conditions

In practice there can be several sufficient definitions for a concept. That is to say several different ways in which a concept could be sufficiently defined by different sets of defining relationships For example:

Gastric ulcer is defined as follows:

This is a sufficient definition because any 56208002 | ulcer| in a 69695003 | stomach structure| is by definition a 397825006 | gastric ulcer| . Based on this definition:

Any postcoordinated expression that specified a disease involving an 56208002 | ulcer| with 363698007 | finding site| 69695003 | stomach structure| would be equivalent to or a subtype of 397825006 | gastric ulcer|  

However, a query for all disorders involving 78653002 | gastric mucosa| would incorrectly exclude 397825006 | gastric ulcer| as the site is specified as 78653002 | gastric mucosa| which is more specific than 69695003 | stomach structure| . In reality there is another sufficient set defining relationships

but this is not currently represented in SNOMED CT. The reason for this is that currently the profile of description logic used by SNOMED CT does not support representation of multiple sufficient sets. 

When multiple sufficient sets are supported, satisfying a single sufficient set enables an inference to be made that all necessary conditions must also be true. For example

However, as the current profile does not enable recognition of multiple sufficient sets, the general rule is to represent the most general sufficient set as this gives the greatest coverage for subsumption testing. This approach is taken because including more defining relationships, without distinguishing them from the sufficient set means some logically equivalent expressions will not compute as equivalent to or subsumed by the defined concept. This occurs in any cases where the expression does not include one of the attributes in the definition - even if it was not part of the logically sufficient set.

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