An SNMP RFC defines the concept of MAX-ACCESS which is a closely related to the classification you describe, but a bit stricter and explicit. Quoting the spec ...
The MAX-ACCESS clause, which must be present, defines whether it
makes "protocol sense" to read, write and/or create an instance of
the object, or to include its value in a notification. This is the
maximal level of access for the object. (This maximal level of
access is independent of any administrative authorization policy.)
The value "read-write" indicates that read and write access make
"protocol sense", but create does not. The value "read-create"
indicates that read, write and create access make "protocol sense".
The value "not-accessible" indicates an auxiliary object (see Section
7.7). The value "accessible-for-notify" indicates an object which is
accessible only via a notification (e.g., snmpTrapOID [5]).
These values are ordered, from least to greatest: "not-accessible",
"accessible-for-notify", "read-only", "read-write", "read-create".