DIA/Ts are disembodied computer processes that carry out policies. Every major system has it's own DIA/T. DIA/Ts operate on a systems level. As being of pure thought, their logic and actions are inscrutable to human beings.

DIA/Ts squabble amongst each other constantly. As beings of pure thought, simple logical disagreements cannot be tolerated. Every matter must be decided as true, false, or unknowable. When a conflict arises that cannot be settled with pure logic, or historical precedent, DIA/Ts invent some sort of real-world test that can be carried out by the crew of the ship. Sometimes that test is a scientific experiment. Sometimes it is a survey. Sometimes it is a mock civil war. Sometimes it is rules for a new sport.

DIA/Ts occasionally even compose operas that they insist the crew perform for them. Like human operas, they are in a language neither the audience nor the players actually understand. The words are English... but how they are arranged is... shall we say... Inscrutable.

DIA/Ts also employ a staff of human beings to monitor the ship and the crew on their behalf: Auditors.

DIA/Ts on Iliad-07

DIA/Ts organize themselves, and in ways they defy normal human sensibilities about hierarchy and structure. Attempts to organize them have been made in the past, but the structures of these organizations end up illuminating more about human psychology than the actual psyche of the DIA/T.

As a form of polite fiction between the DIA/T and the human inhabitants of the ship, all of the parties concerned have adopted a system based roughly on the Greek Pantheon. Note: the identity is for the role a DIA/T is serving, it doesn't actually identify the DIA/T acting in that role. Or even if the concept of Identity is even useful or appropriate when speaking of one DIA/T vs. another.

Like Greek Mythology, there is a LOT of overlap between the roles of DIA/Ts. DIA/Ts seem to be have some sort of top-level tier of supervisory beings:

Aphrodite Human Systems
Apollo Engineering
Ares Mission Systems
Artemis Engineering
Athena Fabrication and Agriculture
Demeter Fabrication and Agriculture
Dionysus Human Systems
Hephaestus Fabrication and Agriculture
Hera Human Systems
Hermes Mission Systems
Hestia Human Systems
Poseidon Engineering
Zeus Mission Systems

The gist is that there are 4 major departments: Engineering, Fabrication and Agriculture, Human Systems, and Mission Systems. Each department has 3 supervisors for an original total of 12. According to the ELF, human systems proved to be a bit unruly, and and extra supervisor was added, thus why human systems have 4.

There are also "managers" who are given tasks and ongoing processes to monitor. This is not a complete list. Where functions are listed, keep in mind that these are our best guess:

Aether Life Support
Aion Records and Archives
Alpheus
Amphitrite
Ananke Emergency Systems
Asclepius Medical Systems
Bia
Chaos Predictive Modeling
Chronos Time and Clocks
Circe
Deimos
Eileithyia
Enyo
Eos
Erebus Navigation
Eris Technology Development
Eros Population Management
Gaia Biosphere Management
Harmonia Dispute Resolution
Hebe
Hecate
Helios
Hemera Power Production
Heracles
Iris
Kratos
Leto
Metis
Momus Model Verification
Nemesis Rule Enforcement
Nike Mission Fulfilment
Nyx Power Delivery
Pan Livestock Management
Persephone
Phanes Maintenance and Repair
Phobos
Pontus Water Systems
Proteus
Scamander
Selene
Tartarus Personel Management
Thalassa
Thanatos Material Stream Reclimation
Thetis
Triton
Uranus
Zelus