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

A Definition that is Both Necessary and Sufficient

The definition shown in 

• 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 

    Concept
    t 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.

Stated view of the definition of |Laparoscopic repair of hernia|

=== 71388002 |Procedure| :
            { 363700003 |Direct morphology| = 414402003 |Hernial opening (morphologic abnormality)|, 
              425391005 |Using access device| = 86174004 |Laparoscope, device|, 
              260686004 |Method| = 257903006 |Repair - action| }

The definition shown in 

• The === symbol indicates that the concept definition is equivalent to the concept. 
  • This means that each of the assertions in the definition necessarily true for all instance of the concept 

    Concept
    t 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.

A Definition that is Necessary but Not Sufficient

The definition shown in 

• The <<< symbol indicates that the concept is a subtype of the concept definition. 
  • This means that each of the assertions in the definition is necessarily true for all instance of the concept 

    Concept
    t 173574009 |Acute benign pericarditis (disorder)|

    .
  • However, this definition is not sufficient, because it is represent a more general meaning. Put another way, it does not capture one or more distinguishing features or the

    Concept
    t 173574009 |Acute benign pericarditis (disorder)|

    . This means that even if all the assertions are true, it may or may not be this concept or one of its subtypes.

Stated view of the definition of |Acute benign pericarditis|

<<< 64572001 |Disease| :
        263502005 |Clinical course| = 424124008 |Sudden onset AND/OR short duration|
            { 116676008 |Associated morphology | = 4532008 |Acute inflammation| , 
              363698007 |Finding site| = 24949005 |Pericardial sac structure| }

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

The definition shown in 

• The >>> symbol indicates that the concept definition represents a subtype of the concept definition. 
  • This means that each of the assertions in the definition is necessarily true for all instance of the concept 

    Concept
    t 173574009 |Acute benign pericarditis (disorder)|

    .
  • However, this definition is not sufficient, because it is represent a more general meaning. Put another way, it does not capture one or more distinguishing features or the 

    Concept
    t 173574009 |Acute benign pericarditis (disorder)|

    . This means that even if all the assertions are true, it may or may not be this concept or one of its subtypes.

Possible stated view of the definition of |Secondary diabetes mellitus|

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

Sufficiently Defined

1. Glossary include
   Gloss sufficiently defined concept Suffix is Def inline Example true Note true Prefix A

   •  If a concept has a sufficient definition, it is possible to infer whether another concept or a 

     Gloss
     PreSpace false t postcoordinated expression

      is a 

     Gloss
     PreSpace false t subtype

      of, or equivalent to, that

     Gloss
     PreSpace false t concept.

     
     
     

2. Primitive

   Glossary include
   Gloss primitive concept Suffix is Def inline Example true Note true Prefix A

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.

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

Gastric ulcer is defined as follows:

397825006|gastric ulcer| 
===	 116680003 |is a| = 64572001 |disease| 
	    { 116676008 |associated morphology| = 56208002 |ulcer| , 
	    363698007 |finding site| =69695003 |stomach structure| }

This is a sufficient definition because any

Any

However, a query for all disorders involving

397825006|gastric ulcer| 
===	 116680003 |is a| = 64572001 |disease| 
	    { 116676008 |associated morphology| = 56208002 |ulcer| , 
	    363698007 |finding site| = 78653002|gastric mucosa| }

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

• The definition

  Concept
  t 363698007|finding site|

  =

  Concept
  t 78653002|gastric mucosa| ShowFormat inline

  is a necessary condition for

  Concept
  t 397825006|gastric ulcer|

  :

  • This is true because all gastric ulcers necessarily involve the

    Concept
    t 78653002|gastric mucosa|

• The definition

  Concept
  t 116676008|morphology|

  =

  Concept
  t 56208002|ulcer| ShowFormat inline

  and

  Concept
  t 363698007|finding site|

  =

  Concept
  t 69695003|stomach structure| ShowFormat inline

  is a sufficient definition for

  Concept
  t 397825006|gastric ulcer|

  :

  • This is true because any ulcer in a stomach structure is a

    Concept
    t 397825006|gastric ulcer|

• Therefore, an assertion that a person has an

  Concept
  t 56208002|ulcer| ShowFormat inline

  with

  Concept
  t 363698007|finding site| ShowFormat inline

  Concept
  t 69695003|stomach| ShowFormat inline

  is sufficient to imply that they have a

  Concept
  t 397825006|gastric ulcer|

  :

  • Since a gastric ulcer necessarily involves the

    Concept
    t 78653002|gastric mucosa| ShowFormat inline

    it should be possible to deduce that a person with an "ulcer" with finding site

    Concept
    t 69695003|stomach| ShowFormat inline

    has a disorder of with a site

    Concept
    t 78653002|gastric mucosa|

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.