Guidelines for equivalence axioms

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Note: Equivalence Axioms (or Logical Definitions) used to be referred to as 'cross-products', but we have largely abandoned this nomenclature.

Equivalence Axioms

Equivalence Axioms, also known as Logical Definitions (LD), are computable logical definitions that complement the existing text definitions. Equivalence Axioms enable tools to access the data and perform tasks and analyses that would be time-consuming and work intensive for humans. One aspect that can aid automated access to the ontology is creating

Structure of Equivalence Axioms

Equivalence Axioms are in the genus-differentia form, such that an equivalence axiom consists of:

  • a genus: the broader class to which the term belongs, and
  • one or more differentia: the property/ies that distinguish the term from other members of the same class.


  • mitochondrial DNA replication is DNA replication that occurs in a mitochondrion
    • genus: 'DNA replication'
    • differentia: 'occurs in' some mitochondrion
id: GO:0006264
name: mitochondrial DNA replication
namespace: biological_process
def: "The process in which new strands of DNA are synthesized in the mitochondrion." [GOC:ai]
is_a: GO:0006261 ! DNA-dependent DNA replication
intersection_of: GO:0006260 ! DNA replication
intersection_of: occurs_in GO:0005739 ! mitochondrion
  • lysosomal membrane is the membrane that surrounds a lysosome
    • genus: 'whole membrane'
    • differentia: and 'bounding layer of' some lysosome

id: GO:0005765
name: lysosomal membrane
namespace: cellular_component
def: "The lipid bilayer surrounding the lysosome and separating its contents from the cell cytoplasm." [GOC:ai]
is_a: GO:0005774 ! vacuolar membrane
intersection_of: GO:0098805 ! whole membrane
intersection_of: bounding_layer_of GO:0005764 ! lysosome
relationship: part_of GO:0005764 ! lysosome
 These definitions of terms created by combining other terms with relations are called cross-products in GO parlance. In the OBO 1.2 (NOTE: CURRENT VERSION is 1.4 ???? 1.4 according to GO website but GO-edit states 1.2) format file, the human-readable text definition is held in the def line, and the cross-product definition in the intersection_of lines of a stanza. The cross-products above would be represented as follows:

Types of differentia classes allowed

Differentia can be made with terms from ontologies other than GO.


  • megasporocyte nucleus is a nucleus that is part of a megasporocyte
id: GO:0043076
name: megasporocyte nucleus
namespace: cellular_component
def: "The nucleus of a megasporocyte, a diploid cell that undergoes meiosis to produce four megaspores, and its descendents." [GOC:jl, ISBN:0618254153]
synonym: "megaspore mother cell nucleus" EXACT []
is_a: GO:0005634 ! nucleus
intersection_of: GO:0005634 ! nucleus
intersection_of: part_of PO:0000431 ! megasporocyte
  • osteoblast development is cell development that results in the complete development of an osteoblast
id: GO:0002076
name: osteoblast development
namespace: biological_process
def: "The process whose specific outcome is the progression of an osteoblast over time, from its formation to the mature structure. Osteoblast development does not include the steps involved in committing a cranial neural crest cell or an osteoprogenitor cell to an osteoblast fate. An osteoblast is a cell that gives rise to bone." [GOC:dph]
is_a: GO:0048468 ! cell development
intersection_of: GO:0032502 ! developmental process
intersection_of: results_in_development_of CL:0000062 ! osteoblast
relationship: part_of GO:0001649 ! osteoblast differentiation

Equivalence Axioms must be 'necessary and sufficient' to define a GO class

 THIS IS NOT CLEAR TO ME: Are we saying that part_of is a necessity condition? 
  • In GO, some relationships assert classification (a nucleolus is a class of organelle), others make statements about necessary conditions for being a member of a class (being part of a nucleus is a necessary condition of being in the class nucleolus).
  • Other relationships specify both necessary and sufficient conditions for being a class member (any channel activity that transports ions is an ion channel activity). Along with reasoning software, we can use these to automate classification.

Molecular function

Equivalent axioms for MF that include 'binding': use 'has_part' some binding (see

When to add an equivalence axiom

An equivalence axiom can be added when there is a criteria that can be specified that distinguishes the GO class from its parent and siblings. Hence, top-level classes cannot have equivalence axioms, since a genera from GO is needed.

Equivalence axioms for specific GO classes

Molecular function


Children of transcription regulator activity

For example: DNA-binding transcription factor activity

transcription regulator activity 'part of' some 'regulation of transcription, DNA-templated' 'has necessary component activity' some 'transcription regulatory region sequence-specific DNA binding'

  • Discussion GO editors 2019-05-06: We should only add 'capable of' MF when there is an emerging function
  • in this case these are different functions, not some emerging function of the complex. We would capture a logical definition only if there is one overall function for the complex.

Biological processes

x biosynthesis

'biosynthetic process'

and ('has primary output' some x)

Can add individual reactions as subclasses

Using the reasoner in Protégé

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