Logical Regression for Planning with Axioms

How should an agent decide when and how to plan? A dominant approach builds agents as reactive policies with adaptive computation (e.g., chain-of-thought), trained end-to-end expecting planning to emerge implicitly. Without control over the presence, structure, or horizon of planning, these systems dramatically increase reasoning length, yielding inefficient token use without reliable accuracy gains. We argue efficient agentic reasoning benefits from decomposing decision-making into three systems: simulative reasoning (System II) grounding deliberation in future-state prediction via a world model; self-regulation (System III) deciding when and how deeply to plan via a learned configurator; and reactive execution (System I) handling fine-grained action. Simulative reasoning provides unified planning across diverse tasks without per-domain engineering, while self-regulation ensures the planner is invoked only when needed. To test this, we develop SR$^2$AM (Self-Regulated Simulative Reasoning Agentic LLM), realizing both as distinct stages within an LLM's chain-of-thought, with the LLM as world model. We explore two instantiations: recording decisions from a prompted multi-module system (v0.1) and reconstructing structured plans from traces of pretrained reasoning LLMs (v1.0), trained via supervised then reinforcement learning (RL). Across math, science, tabular analysis, and web information seeking, v0.1-8B and v1.0-30B achieve Pass@1 competitive with 120-355B and 685B-1T parameter systems respectively, while v1.0-30B uses 25.8-95.3% fewer reasoning tokens than comparable agentic LLMs. RL increases average planning horizon by 22.8% while planning frequency grows only 2.0%, showing it learns to plan further ahead rather than more often. More broadly, learned self-regulation instantiates a principle we expect to extend beyond planning to how agents govern their own learning and adaptation.

Many LLMs plan before they act, yet planning and execution are often still entangled in one long generation trace, enforced only through prompts, or split across separate components. We argue that these two stages call for different computation: planning benefits from diversity and breadth, whereas execution demands precision and faithful adherence to a chosen strategy. Treating them as a single undifferentiated chain wastes tokens on routine derivation and makes it costly to explore alternative strategies at test time. We present the \textbf{Explore-Execute Chain (E\textsuperscript{2}C)}, which keeps both stages in one model but separates them structurally: a stochastic \textit{Exploration} phase drafts a concise high-level plan, and a deterministic \textit{Execution} phase carries it out. Causal SFT and RL train this split so that exploration stays informative and execution remains plan-faithful. Once plans are short yet decisive, extra inference compute can be directed to exploration rather than to repeatedly decoding full solutions. On AIME'2024 at $K{=}32$, \textbf{E\textsuperscript{2}C-ReAct Loop} reaches 53.3% accuracy with only 12.4k tokens, outperforming Tree-of-Thoughts ($N{=}32$: 50.0%, 71.3k). The same structure also supports lightweight domain adaptation: \textbf{Exploration-Focused SFT (EF-SFT)} updates only the planning phase, uses 3.5% of the tokens required by standard SFT, and improves medical benchmark accuracy by up to 14.5%.

Planning over Temporal Dynamic Knowledge Graphs (TDKGs) presents theoretical challenges in open-world environments with incomplete information. Existing action formalisms often face decidability issues and the Ramification Problem, while structural abduction requires expansive combinatorial search spaces. We introduce a unified framework with two modules--PIE-Abducer (incremental direct-derivation abduction) and PIE-APT (Abductive Planning for TDKGs)--operating natively on the expressive SROIQ Description Logic. Modeling state transitions as non-monotonic updates to deductively closed DL theories, we represent actions natively in OWL. This leverages an incremental reasoner to preserve decidability and natively bypass the Ramification Problem. To address incomplete knowledge, PIE-Abducer circumvents Minimal Hitting Set (MHS) enumeration. Instead of combinatorial search, it injects the logical negation of a goal into a consistent DL branch and synthesizes missing premises via direct refutation consequences. PIE-APT employs a recursive Generate-and-Test architecture, interleaving backward-chaining A* search with PIE-Abducer to synthesize both action sequences and abductive assumptions. Candidates undergo strict validation via forward-chaining Temporal Projection to evaluate logical trajectories. We evaluate four OWL benchmarks targeting semantic abilities missing from classical planning: parameterized goals with witness search, mid-search DL entailment, open-world assumption injection, and adversarial plan synthesis. Results show qualitative superiority over classical planners and prove our direct-derivation approach significantly outperforms an MHS-faithful baseline in abductive enrichment.