The General Harvard Separation Axiom (Execution Semantics Theory)

Properties:

Let G be a theory that formally defines execution semantics (domains, contexts, authority). Let O be any theory of computational behavior.

• If O models computation, then O requires execution to occur.
• Therefore O implicitly depends on G's primitives (execution must be defined for computation to be theorized).
• G does not depend on O (execution semantics are primitive, not derived from computational models).

Conclusion:

We cannot derive G from O without circularity:

• Deriving execution semantics from O would mean "execution depends on a theory that assumes execution exists"
• This creates an impossible circular dependency
• Therefore G must be axiomatic - a foundational primitive that cannot be reduced to other computational theories

Any attempt to make G = O or G ⊆ O fails because O already assumes G's primitives exist.

Author:

• Amlal El Mahrouss - amlal@nekernel.org