Policy composition belongs to a specific engine

In an allow-list model, a request can fail because no applicable grant exists. An explicit deny is a separate policy statement that may override grants if the engine defines that behavior. AWS IAM documents explicit-deny precedence in its applicable evaluation logic, while the details of identity policies, resource policies, boundaries, sessions, and organizations vary with context. Do not reduce all AWS requests to one unqualified union or intersection formula; principal and resource-policy cases matter.

Kubernetes RBAC provides a useful contrast: its permissions are additive and it does not express RBAC deny rules. Removing one RoleBinding does not remove permission supplied by another binding. Other configured Kubernetes authorization mechanisms have their own evaluation behavior, which is not the same as adding a fictional deny field to a Role. Read the active engine's rules and distinguish an RBAC grant from the final request outcome in a broader authorization configuration.

For a small teaching model, define an identity grant A, a mandatory boundary B, and an applicable explicit deny D. Permit a request only when both grant and boundary allow and no deny applies. This resembles one restricted category of deny-overrides reasoning, but it is not a complete implementation of AWS IAM. State that resource-based grants, special principals, session policies, organizational controls, and service-specific rules are outside the toy model before using its truth table.

A permissions boundary is generally a maximum permission constraint in the relevant provider model, not an independent grant. Replacing an intersection with a union can create access the administrator never intended. Conditions also matter: a deny statement that does not match the request context is not an applicable deny. Evaluate concrete action-resource-context combinations and test both matching and nonmatching conditions rather than counting how many Allow or Deny words occur in policy files.

Write a matrix of principals, actions, resources, and context values with expected results. Include an allow with no boundary match, an explicit deny matching only one region or resource, and an overlapping grant from another source. Test using the provider's actual policy tools and effective permissions where available, then verify the live service path. A policy simulator's scope may omit controls that affect real requests, so record its coverage instead of treating a green simulation as a universal access proof.

The probability lab is a contrast with deterministic policy decisions. Reset and set both p=0.5, n=10, predict five successes on average, then inspect. It does not evaluate grants, denies, or boundaries. A policy match is not an independent coin flip, and adding more allow statements does not mean increasing a success probability under every engine. Use the distinction to explain why a truth table and concrete matching context are stronger evidence than a plausible-looking aggregate permission percentage.