What does this equation mean?

The planner underneath Shakey was STRIPS — the Stanford Research Institute Problem Solver — described by Fikes and Nilsson in a 1971 paper in the journal Artificial Intelligence . STRIPS represented the world as a set of predicate-logic statements, represented each available action as an operator with a precondition list, a delete list, and an add list, and used a resolution theorem prover guided by means-ends analysis to search for a sequence of operators connecting the current state to a goal state [ 2 ] . Formally, for a state s represented as a set of ground predicates and an operator a with precondition set $\mathrm{pre}(a)$ , delete set $\mathrm{del}(a)$ , and add set $\mathrm{add}(a)$ , the operator is applicable when its preconditions hold, and produces a new state by $\mathrm{pre}(a) \subseteq s \;\Longrightarrow\; \delta(s,a) = \big(s \setminus \mathrm{del}(a)\big) \cup \mathrm{add}(a)$. This is worth writing out because it is a real, load-bearing assumption rather than notation for its own sake: everything about the world not explicitly named in an operator’s delete or add list is assumed to persist unchanged. Without that assumption, an operator’s author would have to state every fact that stays true across every action — combinatorially unworkable. With it, STRIPS could plan efficiently inside a closed, fully modeled world. The same assumption is also the reason planners of this kind struggled the moment they left one: any real-world consequence the plan’s author forgot to encode simply did not exist for the planner, and a divergence between the model and the actual room meant replanning from scratch rather than adapting mid-execution.