Formal Verification of AI Safety Policies

Formal verification uses mathematical proof to demonstrate that a system satisfies certain properties for all possible inputs. When applied to AI safety policies, it can prove that no action envelope exists that would violate a specified safety invariant. This is stronger than testing, which can only show the absence of bugs for the specific cases tested.

What Can Be Verified

Policy evaluation is a deterministic function from envelopes to decisions. This makes it amenable to formal analysis. Properties that can be verified include:

Completeness: Every possible envelope produces a defined decision (no undefined states).

Consistency: No envelope produces both allow and deny simultaneously (conflict-free resolution).

Safety invariants: Specific actions are always denied regardless of other rule combinations. For example: "data.delete on production resources is always denied."

Monotonicity: Adding rules only restricts behavior (adding a deny rule never causes an allow).

Approaches

Model Checking

Encode the policy and the policy engine's evaluation logic as a formal model. Use a model checker (like TLA+ or Alloy) to exhaustively verify properties against all possible inputs within a bounded domain.

Model checking is effective for small to medium policy sizes. The state space grows with the number of rules and possible attribute values, so very large policies may require bounded verification rather than complete verification.

SMT Solving

Encode policy rules as logical constraints and use an SMT (Satisfiability Modulo Theories) solver to check whether a violating input exists. If the solver proves no satisfying assignment exists, the property holds for all inputs.

// Does there exist an envelope E such that:
// - E.action = "data.delete"
// - E.resource matches "production/*"
// - policy(E) = "allow"
// If UNSAT: the safety property holds

Type-Level Verification

Use a language with a powerful type system (like TypeScript's conditional types or Rust's trait bounds) to encode policy constraints at the type level. This catches certain classes of errors at compile time.

Practical Limitations

Formal verification proves properties of the model, not the implementation. If the model does not accurately reflect the implementation, the proof does not apply. Bridge this gap by generating the implementation from the model or by verifying the implementation directly.

When to Use Formal Verification

Formal verification is most valuable for core safety invariants that must never be violated. It is less practical for complex conditional rules where the state space is too large for exhaustive analysis. Use it for the properties that matter most and supplement with testing for everything else.

Formal verification provides the strongest assurance. For the most critical safety properties, nothing less should suffice.