Anti-Goal Reasoning: Rethinking the Theory of Goal Reasoning in Non-Axiomatic Logic

In both cognitive science and computer science, goals are conceptualized as cognitive states that flexibly combine with world knowledge to organize and specify purposeful behavior. In this way, goals are compositional representations whose content relates to rational behavior. We here draw attention to goals as representations and their content because it highlights a parallel with other areas in cognitive science - in particular, the syntax-semantics interface in linguistics and logic - while also foregrounding foundational questions about the expressivity, design, and efficiency of different goal representations. For example, goals are typically taken as fixed and imposing constraints on desirable behaviors, but we can also identify constraints on goal representations themselves, such as whether a particular goal language is sufficiently expressive to capture behaviors of interest, or whether different goal representations capture the same behavior. Here, we synthesize work that aims to characterize the properties of different goal representations and suggest these are points of a broader design space. We close by discussing how distinguishing the form and meaning of goals can elucidate the implicit assumptions we make about goals, inform the study of interactions between higher-level cognition and motivation, and isolate axes of variation for different conceptions of goals.

Large language models perform well on many reasoning tasks, yet they often lack awareness of whether their current knowledge or reasoning state is complete. In non-interactive puzzle settings, the narrative is fixed and the underlying structure is hidden; once a model forms an early hypothesis under incomplete premises, it can propagate that error throughout the reasoning process, leading to unstable conclusions. To address this issue, we propose SABA, a reasoning framework that explicitly introduces self-awareness of missing premises before making the final decision. SABA formulates reasoning as a recursive process that alternates between structured state construction and obstacle resolution: it first applies Information Fusion to consolidate the narrative into a verifiable base state, and then uses Query-driven Structured Reasoning to identify and resolve missing or underspecified premises by turning them into queries and progressively completing the reasoning state through hypothesis construction and state refinement. Across multiple evaluation metrics, SABA achieves the best performance on all three difficulty splits of the non-interactive Detective Puzzle benchmark, and it also maintains leading results on multiple public benchmarks.

Large language models generate computationally expensive yet semantically void reasoning on beyond-capability tasks, creating risks where plausible-sounding but incorrect derivations mislead users. We characterize this \textit{futile reasoning} phenomenon through systematic analysis, revealing universal capability overreach and systematic miscalibration between capability and behavior. The dominant failure mode is specious reasoning, which outputs look superficially valid but contain subtle errors, escalating with task difficulty. To address this, we introduce \textbf{CaRL} (\textbf{Ca}pability-\textbf{a}ligned \textbf{R}einforcement \textbf{L}earning), which aligns model behavior with capability boundaries through reward shaping that incentivizes refusal over futile reasoning and hindsight refusal augmentation that converts failures into refusal supervision. Experiments demonstrate a substantial reduction in futile reasoning while preserving performance across task difficulties, effectively achieving capability-aligned behavior without sacrificing utility. \footnote{https://github.com/icip-cas/Knowing-When-to-Quit}