TLDR: This research introduces a novel approach to automated planning that addresses the limitation of the Domain Closure Assumption (DCA), which typically assumes a fixed set of objects. By formulating planning problems in first-order logic within the situation calculus, the authors propose a method for “bounded proper planning” where objects can be dynamically created or destroyed. Their A*-based heuristic planner, implemented in PROLOG, demonstrates soundness and completeness for these complex scenarios, enabling planning in environments with incomplete knowledge and evolving object sets, albeit with computational challenges as the number of dynamic objects increases.
Automated planning, a core area of artificial intelligence, traditionally operates under a significant simplification: the Domain Closure Assumption (DCA). This assumption dictates that all objects relevant to a planning problem are known and fixed from the outset. However, the real world is far more dynamic, with objects constantly being created, destroyed, or changing in ways that cannot be predicted in advance. This limitation has posed a considerable challenge for planners aiming to tackle more realistic scenarios.
A new research paper, Planning with Dynamically Changing Domains, by Mikhail Soutchanski from Toronto Metropolitan University and Yongmei Liu from Sun Yat-sen University, introduces a groundbreaking approach to overcome this hurdle. Their work focuses on developing a planning framework that can handle environments where the set of objects changes dynamically as actions are performed.
Addressing the Dynamic World
The core innovation lies in formulating the planning problem using first-order logic within the framework of the Situation Calculus. Unlike traditional methods that rely on a complete, finite list of objects, this approach assumes an initial theory that is a finite, consistent set of ‘fluent literals’ – essentially, known facts about the world. This allows for incomplete knowledge about the initial state and, crucially, permits objects to be created or destroyed during the planning process.
The researchers define a specific type of problem called ‘bounded proper planning’ (BPP). This involves finding a plan (a sequence of actions) within a predefined length limit, ensuring that the plan works across all possible interpretations (models) of the initial, incomplete knowledge. A key insight that makes this feasible is proving that, even with dynamic object creation and destruction, at any given planning step, there are only a finite number of possible actions that can be considered. This ‘finiteness’ is critical for the search algorithm to remain tractable.
How the Planner Works
To navigate the vast possibilities of dynamically changing domains, the proposed planner employs an A* search algorithm. This algorithm intelligently explores sequences of actions, guided by a heuristic function inspired by the well-known FF planner. The heuristic helps estimate how close a particular sequence of actions is to achieving the desired goal, making the search more efficient.
The system handles the evolution of the world through a process called ‘progression.’ After each action, the initial theory is updated to reflect the new state of affairs, including any newly created objects or those that have ceased to exist. This allows the planner to reason forward and adapt to the changing environment.
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Proof-of-Concept and Challenges
The researchers developed a proof-of-concept implementation of their planner in PROLOG. They tested it on several benchmarks, including a modified version of the British TV show ‘Countdown’ (where numbers are created and destroyed), an ‘Infinite Blocks World’ (where blocks can be brought into existence or merged), and a new ‘Mixers’ benchmark (involving mixing ingredients to create new compounds). The experiments demonstrated the planner’s ability to solve problems without the Domain Closure Assumption, a significant step forward.
However, the research also highlights the inherent computational intensity of planning with dynamically changing objects. As the number of created or destroyed objects grows, the combinatorial possibilities increase rapidly, making more complex instances challenging to solve within reasonable timeframes. This suggests that while the theoretical foundation is sound, further work is needed to design more efficient programs for these complex planning scenarios.
This research represents an important contribution to automated planning, moving the field closer to tackling real-world problems where the environment is not static but constantly evolving. It opens doors for future planners that can operate effectively in truly open and dynamic worlds.
