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Use backward deletion of achieved goal requirements; this decides precondition-free ground STRIPS planning in polynomial time. Let $I$ be the initial set of true facts, $G$ the positive conjunctive goal set and $\mathcal{A}$ the ground actions. Assume the usual disjoint add and delete lists; if both lists contain a fact, first normalize the net effect according to the action semantics.

Maintain residual goal set $R=G$ and an initially empty list $L$. While $R⊈I$, look for an action $a$ satisfyingIf no such action exists, reject. Otherwise record $a$ in $L$ and replace $R$ by $R\setminus \mathrm{Add}(a)$. When $R\subseteq I$, return the actions in reverse order of recording. All actions are applicable because their precondition sets are empty.

For soundness, the selected action can be put last in a plan for the current residual goals: it supplies the removed goals and deletes none of the goals still being required. Reversing all recorded selections makes the final state satisfy the original $G$.

For completeness, suppose $R$ is not already satisfied initially but a plan achieves it. Consider the last action in that plan that changes any fact of $R$. Its effective changes cannot delete any member of $R$, because no later action repairs it; it must add at least one member. Thus a candidate exists. Moreover any candidate chosen by the algorithm is safe: removing some requirements gives a subset of $R$, so a plan for $R$, if one exists, also establishes the smaller goal set. Appending the chosen last action then restores the removed requirements without harming the rest. Mathematical induction therefore preserves solvability during all choices.

Each successful iteration removes at least one residual goal, so there are at most $|G|$ iterations and the returned plan has at most $|G|$ actions. Scanning all actions and their effect lists per iteration is polynomial in the input size, for example $O(|G||\mathcal{A}||P|)$ with simple fact-set representations over $P$. Merely taking the union of all add effects would be unsound, since actions can delete each other's achievements. This algorithm is the last-achiever algorithm for precondition-free planning.

For an intelligent agent that must perceive a changing world and reason about new combinations of objects and goals, a hybrid of learned representations and structured computation is the most defensible choice. The distinction concerns representation and operations, not whether the implementation is a computer or a biological neural network.

In symbolic computation, identifiable tokens stand for entities, properties or relations, and explicit procedures manipulate structured expressions. A planner might represent $\mathrm{At}(\text{agent},A)$ and apply an action rule with preconditions and consequences. The same rule can apply to different objects by substituting their tokens. Subsymbolic computation instead operates on quantities such as distributed activity vectors and learned connection weights; a concept need not correspond to one independently inspectable token. A neural network can transform an image into an action tendency through many interacting units without an explicit list of logical propositions.

The physical symbol system hypothesis made structured symbolic processing a proposed basis for general intelligence. Its accompanying account of search explains how a system can construct and test candidate solutions. This is a substantive empirical hypothesis about intelligent computation, not a theorem that all intelligent behaviour must have one implementation.^[ref]

Symbolic computation has strong advantages when a task already has a reliable relational description. A route planner can combine a newly learned destination with familiar movement rules, enforce a safety constraint explicitly, and revise a plan after a route is blocked. Its intermediate states can expose why an action is permitted. However, perceptual input does not arrive as a clean set of symbols. Identifying objects, deciding which relations matter and connecting tokens to sensory consequences constitute a symbol grounding problem. Large rule sets also face combinatorial search and brittle assumptions about uncertain or changing situations. Explicit representation does not guarantee that the rules are correct or that the search is tractable.

Subsymbolic computation is attractive for perception and motor coordination because statistical learning can exploit regularities in noisy, high-dimensional observations. Shared features allow a learned representation to generalize across similar inputs, and differentiable models can be optimized jointly with a task objective. Yet good interpolation is not the same as compositional generalization. A system can recognize familiar combinations while failing to recombine a familiar operation with a newly learned primitive. A plausible-looking output also need not satisfy a constraint or reflect calibrated uncertainty.

A useful computational test used artificial navigation commands paired with action sequences. Recurrent sequence models generalized well on ordinary splits but much less reliably on splits requiring systematic recombination of primitives and operators. The controlled split is crucial: high accuracy when train and test combinations resemble one another does not test the same claim as transfer to held-out constructions. This result constrains the tested training procedures and inductive biases; it does not prove that every recurrent neural network is incapable of compositional computation.^[ref]

Evidence also argues against equating useful symbolic structure with a hand-written, deterministic rule book. In one-shot character learning, a probabilistic model represented a character through a generative drawing program and inferred that program from a small amount of evidence. It was tested on recognizing new examples and generating plausible variations, with comparisons to human performance. The study shows how Bayesian inference, reusable parts and structured generative programs can work together; it does not establish a universal advantage over every future deep learner or solve general agency.^[ref]

The two approaches can therefore interact. A learned visual representation can propose objects and uncertain relations; a structured world model can evaluate actions and enforce constraints; sensory prediction errors can revise the representation. Conversely, a neural network can implement operations over structured variables, and a symbolic program can manipulate probabilities and call a learned perceptual module. A binary division into “rules” and “learning” misses these possibilities.

For viability, I would compare intelligent agents under the same sensory inputs, experience budget and action constraints. Tests should include novel combinations, changing goals, noisy observations, transfer after an intervention, and the computational cost of planning. The intelligent agent must learn which aspects of the environment can be trusted and detect when its abstractions fail. Learned distributed computation is particularly useful for acquiring representations; structured, uncertainty-aware computation is particularly useful for flexible recombination and planning. Their integration is a stronger proposal for broad agency than an unsupported claim of universal superiority for either alone.

A world model supports intelligent behaviour by predicting the consequences of actions that need not be executed first. The prefrontal cortex can contribute task-state and goal control, while the hippocampus can supply relational and episodic content for constructing possible situations and trajectories. This is a division of computational requirements, not a rigid one-region-per-function scheme.

In a Markov decision process, a model can represent transitions $\hat{P}(s^{\prime }\mid s,a)$ and expected rewards $\hat{r}(s,a)$. Planning uses them to evaluate an action through a backup such asLonger searches apply the same principle across alternative trajectories. A world model can be symbolic, distributed, probabilistic or a combination; it need only preserve information relevant to the decision. In a partially observed situation, the intelligent agent must infer a state or maintain uncertainty over states rather than treating the latest image as a complete description of the world.

For a simple constructed example, suppose one action leads to food and another to water, with current outcome values $2$ and $1$. After the food is devalued to $0$, an intelligent agent that knows the action–outcome relations can immediately prefer water without experiencing the food-producing action again. A purely cached action value does not necessarily change at that moment. This demonstrates the usefulness of an internal model; it does not imply that every devaluation effect uniquely identifies one algorithm, because inferred state changes or offline value updates can also alter cached decisions.

Mental simulation can recombine remembered components into a possible future, evaluate an untried route and compare goals. It differs from simply replaying a previous trajectory verbatim. It also differs from episodic memory retrieval: simulated content may describe something that never happened. Both operations can use shared representations, so a new imagined situation need not be generated independently of memory.

The prefrontal cortex is well placed to contribute the control side of this process: maintaining the current task, selecting relevant information, representing goals and using prospective outcomes to guide action. It is heterogeneous, and activity in one subregion is not evidence that all of prefrontal cortex carries a complete internal simulator. A particularly relevant hypothesis concerns the orbitofrontal cortex: a useful decision state may depend on previous events and task rules even when current sensory input is unchanged.

A human fMRI study used superimposed face and house images with a rule determining which category to judge from the preceding task history. Different hidden task states could therefore accompany similar current inputs. Cross-validated multivariate decoding recovered task-state information from orbitofrontal cortex, and decoding fidelity related to behavioural accuracy. This supports a role in representing the situation in which values and actions are evaluated. It does not demonstrate that the decoded patterns themselves contain a complete future trajectory, and noninvasive imaging cannot identify the synaptic algorithm.^[ref]

The hippocampus provides a complementary source of spatial and relational content. A cognitive map describes relationships among locations or task states rather than only a sequence of rewarded responses. Such a representation can support a novel route when goals change, and event representations can contribute objects, locations and contextual relations to a simulated scene. Whether an internally generated sequence represents a possible future, a remembered past or a training signal must be tested rather than inferred from sequence-like firing alone.

In freely moving rats choosing journeys between food locations, hippocampal place-cell ensembles sometimes produced internally generated sequences before travel. Decoded sequences described trajectories related to remembered goals and predicted upcoming behaviour. The ordering and timing make the result relevant to prospective computation, but the recording is correlational: a sequence could reflect a prepared choice or goal-related retrieval rather than perform the decisive search itself.^[ref]

A separate intervention interrupted awake sharp-wave ripples during a spatial alternation task and impaired learning and performance. Place fields and post-experience reactivation were relatively preserved, helping distinguish the effect from wholesale destruction of spatial coding or later replay. This supports a causal contribution of awake ripple-associated processing to memory-guided decisions, without identifying every disrupted sequence as a planning calculation.^[ref]

Human lesion evidence extends the discussion beyond navigation. Patients with predominantly bilateral hippocampal damage were asked to construct new experiences from short scenario cues. Their descriptions were generally less spatially coherent than those of matched controls, despite preserved semantic retrieval; one patient performed well. The task therefore supports a hippocampal contribution to binding imagined scene elements, while the spared case, lesion selectivity and the difference between scene construction and action planning limit a universal necessity claim.^[ref]

A plausible integrated model lets prefrontal representations specify the task and current goal, hippocampal and cortical representations generate or retrieve candidate situations, and valuation and action-selection circuits compare their consequences. Communication can be iterative: candidate outcomes change what information is sought, and new observations update the inferred state. This is more specific than assigning “imagination” to the hippocampus and “intelligence” to prefrontal cortex, but remains a hypothesis about their interaction.

Planning also has costs. Long simulations can amplify model errors, and unlimited search is computationally expensive. An intelligent agent should select a useful abstraction, prioritize relevant branches and decide when a cached policy is adequate. Tests should distinguish sensitivity to reward changes from sensitivity to transition changes, and compare neural predictions before a decision rather than only after a successful action. World models enable flexible prospective control; the evidence implicates interacting state, memory and valuation processes, rather than a single anatomical seat of mental simulation.

Computing or comparing sequences of actions using representations of their expected consequences and relevant constraints. A plan can be revised after a goal, transition or inferred state changes. Planning is distinct from merely evaluating one fixed control policy or repeating a cached response.

An approach to automated planning that constructs a Boolean satisfiability problem for a bounded planning horizon, solves it and decodes a satisfying assignment into a plan. A typical encoding has time-indexed action occurrences and planning fluents, initial and goal clauses, action precondition axioms, state-transition constraints and action exclusion axioms. Sequential and parallel encodings have different notions of a step.

Henry Kautz and Bart Selman introduced planning as satisfiability in their 1992 paper.^[ref]

A predicate whose ground facts are unchanged by every action in a planning model. Object types and a fixed adjacency relation are common examples. Static conditions can filter ground actions before search; they need not acquire a separate truth variable at every time layer. A planning fluent can instead be added or deleted by actions.

Computation using explicitly structured representations whose elements have identifiable roles, with rules or procedures acting on those structures. Logical planning is an example. This sense concerns symbolic cognitive architectures rather than only computer algebra; it can be implemented by different physical substrates.

An internal model of relationships among states, actions, observations and outcomes, used to predict consequences or support inference. It can be incomplete and task-specific. Planning through a mistaken model can produce confident errors, so model accuracy and the choice of abstraction are part of intelligent control.