https://www.zhumengyao.com/tags/agentic-ai-notation/Recent content in Agentic AI Notation on AI · Math · ScienceHugoenMon, 24 Aug 2026 00:00:00 +0000https://www.zhumengyao.com/notes/agentic-ai-understanding-instruction-space/Mon, 24 Aug 2026 00:00:00 +0000https://www.zhumengyao.com/notes/agentic-ai-understanding-instruction-space/<h2 id="definition-of-instruction-space">Definition of Instruction Space</h2> <p>An instruction space is the organized set of instructions that may govern, constrain, guide, or otherwise influence the behavior of an AI agent. It can be represented as $I = \{i_1, i_2, \ldots, i_n\}$, where $I$ denotes the instruction space and each $i_j \in I$ denotes a unit instruction expressing an individual rule, requirement, constraint, preference, procedure, condition, or behavioral direction that the agent can interpret and apply. The instruction space may contain instructions originating from different authorized sources or functional levels, such as system instructions $I^{S}$, user instructions $I^{U}$, task instructions $I_{\tau}$, and skill or workflow instructions $I^{K}$, with these instruction sets forming relevant parts of the broader space, for example $I^{S}, I^{U}, I_{\tau}, I^{K} \subseteq I$. The elements of $I$ do not necessarily have equal authority, applicability, or effect: some instructions may apply generally, others only to a particular task $\tau$, state $z_t$, or runtime condition, and some may be overridden, disabled, superseded, or rendered inapplicable according to the governing instruction hierarchy and applicable conditions. Thus, $I$ represents the broader space of instructions potentially relevant to agent behavior, while an active instruction set $I^{*}_{\tau,t} \subseteq I$ can represent the instructions that actually govern or guide the agent for task $\tau$ at execution step $t$.</p>