Policy Algebra for Trust-Preserving Agentic AI Execution

LLM-based agentic frameworks primarily optimize functional capabilities such as reasoning, tool invocation, and task delegation, but in enterprise environments, the reliability of execution against unauthorized data access or unapproved side effects is more critical.

This research defines reliable capability as a path property. An agent is considered to have reliable capability only when it completes tasks through permissible action events under nine constraints: identity, profile, tools, data, memory, budget, artifacts, authorization, and audit.

The proposed policy algebra constructs security profiles and runtime obligations through joins, intersections, budget reductions, authorization inheritance, and evidence accumulation. This composition derives the least restrictive state that satisfies all governance inputs and propagates restrictions even during multi-agent invocations. It also introduces cost-aware artifact materialization, which transitions execution to recoverable outcomes as budget exposure increases.

Evaluation results show that the policy algebra runtime intervened in 94.8% of policy violation events while maintaining a 86.9% task completion rate. It eliminated observed profile monotonicity violations and zero-artifact depletion violations, improving audit completeness to 98.6%. This method provides formal correctness conditions and executable decision semantics from a trust-capability trade-off perspective, rather than a capability benchmark perspective.