The logic definitions are represented by the OWL axiom refset that is a replacement of the RF2 stated relationship file. As a result, the nature of the inferred relationship file in the distribution normal form (DNF) has changed because the new DL features are not representable in the current relationships file. The inferred relationship file will maintain the same format and structure, but it is no longer equivalent to the stated form (containing all necessary and sufficient conditions). In fact, it is a collection of all the necessary conditions of precoordinated concepts and represents a subset of the full semantics.

Necessary Normal Form

The Necessary Normal Form (NNF) is a replacement for the Distribution Normal Form for inferred relationships. The NNF is a precalculated distribution form for practical purposes, for example, to support the continuity of existing implementations based on relational databases and queries by the expression constraint language.

The NNF consists of the full set of necessary relationships of precoordinated concepts after removal of redundant relationships within a given concept definition. Within the scope of a SNOMED CT terminology, necessary relationships are defined only for precoordinated concepts (aka OWL’s named classes). Let C be a precoordinated concept and D be either a precoordinated concept or a complex expression. If an axiom is in the form of SubClassOf(C D) or EquivalentClasses(C D), then all of the derivable and necessary relationships of D are necessary relationships of C.

The NNF does not include class disjointness, transitive properties, reflexive properties and sufficient conditions represented as General Concept Inclusions (GCIs) in the OWL axiom refset.

Rules for determining redundant relationships

Rule 1 - Class and Role inclusions

Given two relationships, A and B, A with r = C and B with s = D, within the same role group, A is redundant if:

• r is the same as or a supertype of s, and

• C is the same as or a supertype of D

Note, “crossover relationships”, where r is a supertype of s, and C is instead a subtype of D do not result in a redundant relationship.

Example for Class inclusion

Stated relationships

Inferred relationships before the removal of redundant relationship

Inferred relationships after the reduction

For |Fracture of radius|, the relationship |Finding site| = |Bone structure of radius and/or ulna| is inherited from |Fracture of forearm|, which is a redundant relationship because |Radius bone structure| is a subtype of |Bone structure of forearm|. The relationship |Associated morphology| = |Traumatic abnormality| is inherited from |Injury of radius|, which is a redundant relationship because |Fracture| is a subtype of |Traumatic abnormality|.

Example in OWL axiom refset and RF2 relationship file (NNF)

Example for Role inclusion

Stated relationships

Inferred relationships before the removal of redundant relationship

Inferred relationships after reduction

For concept |Kidney biopsy|, the relationship 363704007 |Procedure site| = 64033007 |Kidney structure| is inherited from 118851004 |Procedure on kidney|, which is a redundant relationship to 405813007 |Procedure site - Direct| = |Kidney structure| because |Procedure site - Direct| is a subtype of |Procedure site|. Because |Kidney structure| is a subtype of |Urinary system structure| and |Retroperitoneal compartment structure|, the inherited relationships for |Procedure site - Direct| are also redundant.

Example in OWL axiom refset and RF2 relationship file (NNF)

Rule 2 - Property chains including transitive properties

Given attribute r, s and t with a property chain SubObjectPropertyOf(ObjectPropertyChain(t s) r), and two relationships A and B, A with r = C and B with u = D, within the same role group, A is redundant if:

• Attribute u is the same as or a subtype of t, and

• D has relationship to C via attribute s

Note the following:

• C does not need to subsume D

• Attribute t does not need to be the same as or a subtype of r

• Transitive properties are defined by a property chain in the form of

     SubObjectPropertyOf(ObjectPropertyChain(r r) r) and thus it is a special case of the above.

Example for property chain:

Stated relationships

Inferred relationships before the removal of redundant relationship

Inferred relationships after reduction

For |Product containing ethyl morphine|, the relationship |has active ingredient| = |Morphine| is inherited from |Product containing morphine|, which is a redundant relationship to |has active ingredient| = |Ethyl morphine| because |Ethyl morphine| |Is modification of| |Morphine| and |has active ingredient| has a property chain with |Is modification of|.

Example in OWL axiom refset and RF2 relationship file (NNF)