# Necessary Conditions and Sufficient Definitions

This section briefly outlines different aspects of assertions made about concepts and the extent to which they are necessarily true or form part of a sufficient definition of the concept. More detailed illustrations of some of the points on this page are provided in [Necessary and Sufficient - Examples](https://docs.snomed.org/snomed-ct-specifications/snomed-ct-release-file-specification/appendices/appendix-d-concept-definition-illustrations#necessary-and-sufficient-examples).

## Assertions

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.

**Example**

* If you have a [71620000 | fracture of femur|](http://snomed.info/id/71620000) , the morphological abnormality 72704001 <mark style="color:blue;">|</mark>fracture<mark style="color:blue;">|</mark> must be present. Therefore, 116676008 <mark style="color:blue;">|</mark>morphology<mark style="color:blue;">|</mark> <mark style="color:red;">=</mark> 72704001 <mark style="color:blue;">|</mark>fracture<mark style="color:blue;">|</mark> is a *necessary condition* of <mark style="color:blue;">|</mark>fracture of femur<mark style="color:blue;">|</mark>.

## 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.

{% hint style="info" %}
**Notes**

* Any concept that matches the *sufficient definition* is equivalent to or a subtype of the defined concept.
* A 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.
  {% endhint %}

**Examples**

* The following set of assertions is a sufficient definition for [74400008 | appendicitis (disorder)|](http://snomed.info/id/74400008) because any concept for which this set of assertions is true must either be the disorder *appendicitis* or a subtype of *appendicitis*.

{% code overflow="wrap" %}

```
18526009 |disorder of appendix| + 302168000 |inflammation of large intestine| :
    116676008 |associated morphology| = 23583003 |inflammation|, 
    63698007 |finding site| = 66754008 |appendix structure|
```

{% endcode %}

* Both the following sets of assertions are sufficient definitions for the concept [8801005 | Secondary diabetes mellitus (disorder)|](http://snomed.info/id/8801005)

{% code overflow="wrap" %}

```
73211009 |Diabetes mellitus| : 246075003 |Causative agent| = 105590001 |Substance|
73211009 |Diabetes mellitus| : 42752001 |Due to| = 64572001 |Disease|
```

{% endcode %}

While each of the assertions <mark style="color:blue;">|</mark>Causative agent<mark style="color:blue;">|</mark> <mark style="color:red;">=</mark> <mark style="color:blue;">|</mark>Substance<mark style="color:blue;">|</mark> and <mark style="color:blue;">|</mark>Due to<mark style="color:blue;">|</mark> <mark style="color:red;">=</mark> <mark style="color:blue;">|</mark>Disease<mark style="color:blue;">|</mark> form part of a sufficient definition, neither of these assertions are necessary conditions because *only one* of them needs to be true. This illustrates that an assertion that is part of a sufficient definition need not be a necessary condition.

## Concepts with no Sufficient Definitions

A 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

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

A 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)|](http://snomed.info/id/397825006) is an ulcer in a stomach structure:

```
=== 64572001 |disease| : 
    {116676008 |associated morphology| = 56208002 |ulcer|,
    363698007 |finding site| = 69695003 |stomach structure|}
```

However, another definition could be created with a more specific site gastric mucosa:

```
=== 64572001 |disease| : 
    {116676008 |associated morphology| = 56208002 |ulcer|,
    363698007 |finding site| = 78653002 |gastric mucosa|}
```

In both cases these definition are equivalent to <mark style="color:blue;">|</mark>Gastric ulcer (disorder)<mark style="color:blue;">|</mark>. 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

```
=== 64572001 |disease| : 
    {116676008 |associated morphology| = 56208002 |ulcer|,
    363698007 |finding site| = 127869006 |Anterior wall of fundus of stomach|}
```

This satisfies the sufficient definition because the finding site is a subtype of stomach structure. This will therefore classify as a type of <mark style="color:blue;">|</mark>Gastric ulcer (disorder)<mark style="color:blue;">|</mark> 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 <mark style="color:blue;">|</mark>Gastric ulcer (disorder)<mark style="color:blue;">|</mark>. The fact that it is a type of gastric ulcer causes it to inherit <mark style="color:blue;">|</mark>finding site<mark style="color:blue;">|</mark> <mark style="color:red;">=</mark> <mark style="color:blue;">|</mark>gastric mucosa<mark style="color:blue;">|</mark> so it will now be included in the query for disease in the gastric mucosa.

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