mlsanityData to 7 Oct 2026

Structured Abductive-Deductive-Inductive Reasoning for LLMs via Algebraic Invariants

arXiv 2604.15727 ↗First posted 17 Apr 2026cs.AI cs.LG cs.LOcited by 1

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

Large language models exhibit systematic limitations in structured logical reasoning: they conflate hypothesis generation with verification, cannot distinguish conjecture from validated knowledge, and allow weak reasoning steps to propagate unchecked through inference chains. We present a symbolic reasoning scaffold that operationalizes Peirce's tripartite inference -- abduction, deduction, and induction -- as an explicit protocol for LLM-assisted reasoning. The framework enforces logical consistency through five algebraic invariants (the Gamma Quintet), the strongest of which -- the Weakest Link bound -- ensures that no conclusion in a reasoning chain can exceed the reliability of its least-supported premise. This principle, independently grounded as weakest link resolution in possibilistic logic and empirically validated for chain-of-thought reasoning, prevents logical inconsistencies from accumulating across multi-step inference. We verify all invariants through a property-based testing suite of 100 properties and 16 fuzz tests over 10^5+ generated cases, providing a verified reference implementation of the invariants suitable as a foundation for future reasoning benchmarks.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 10 of its 32 references that are in the map. First posted on arXiv 17 Apr 2026.

Builds on

10 of 32 references.

Closest ancestors · 2

Same direction, newest first

  1. 2025Typed Chain-of-Thought: A Curry-Howard Framework for Verifying LLM Reasoning1 Oct
  2. 2022FOLIO: Natural Language Reasoning with First-Order Logic2 Sep

Other references · 8

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  2. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
  3. 2023Let's Verify Step by Stepcited by 3,598
  4. 2020Logical Neural Networkscited by 118
  5. 2024A Chain-of-Thought Is as Strong as Its Weakest Link: A Benchmark for Verifiers of Reasoning Chainscited by 63
  6. 2026AIRS-Bench: a Suite of Tasks for Frontier AI Research Science Agentscited by 32
  7. 2026Epistemology gives a Future to Complementarity in Human-AI Interactionscited by 5
  8. 2026AI-Assisted Engineering Should Track the Epistemic Status and Temporal Validity of Architectural Decisionscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Position: Evaluation Scores Are Perishable Knowledge Claimscited by 3

Similar, not cited

Close in wording, no citation either way

  1. 2024Leveraging LLMs for Hypothetical Deduction in Logical Inference: A Neuro-Symbolic Approach
  2. 2026Beyond Surface Forms: Symbolic Edits as a Test for Logical Reasoning with LLMs
  3. 2024Disentangling Logic: The Role of Context in Large Language Model Reasoning Capabilities
  4. 2024Inductive or Deductive? Rethinking the Fundamental Reasoning Abilities of LLMs
  5. 2025LogiDynamics: Unraveling the Dynamics of Inductive, Abductive and Deductive Logical Inferences in LLM Reasoning
  6. 2025From Hypothesis to Premises: LLM-based Backward Logical Reasoning with Selective Symbolic Translation
  7. 2024A Closer Look at Logical Reasoning with LLMs: The Choice of Tool Matters
  8. 2026Discovering a Shared Logical Subspace: Steering LLM Logical Reasoning via Alignment of Natural-Language and Symbolic Views