actsuchP

ActsuchP is a theoretical construct in action selection and automated planning that describes a constraint-driven rule for choosing actions whose execution guarantees that a given predicate P holds in the resulting state within a specified context.

Origin and terminology: The term actsuchP is a portmanteau of "act" and "such that," reflecting its roots in constraint-based reasoning. It has appeared in theoretical discussions of planning and formal methods since the early 2010s, with formalizations in AI textbooks and research papers on predicate-guided action selection.

Formal framework: Let s be the current state, A a set of available actions, PRE(a) the precondition of action a, and E(a, s) the state transition function. actsuchP selects actions a in A such that PRE(a) holds in s and P(s') holds, where s' = E(a, s). Some formulations require P to hold throughout the execution trace, others only in the final state.

Variants: Strong actsuchP requires P to hold after every intermediate step; weak actsuchP requires only the final state; soft actsuchP allows P to be violated with a penalty measure.

Applications: Used in planning algorithms to enforce safety or goal conditions, in robotics for task execution under constraints, and in model checking to generate constraint-satisfying scenarios.

Limitations and critique: The approach can be computationally intensive, depends on accurate modeling of actions, and may reduce the space of feasible plans if P is overly restrictive.

See also: predicate logic, constraint satisfaction problem, conditional planning, action languages.