SIGNALAI·Jun 24, 2026, 4:00 AMSignal75Medium term

HOLMES: Evaluating Higher-Order Logical Reasoning in LLMs

Source: arXiv cs.AI

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HOLMES: Evaluating Higher-Order Logical Reasoning in LLMs

arXiv:2606.23238v2 Announce Type: replace Abstract: Logical reasoning is essential for reliable AI, yet existing benchmarks are largely first-order-logic-centric, focusing on object-level deduction over fixed predicates. This misses many realistic scenarios where models must reason over rules, predicates, functions, constraints, and decision procedures themselves. We introduce HOLMES (Higher-Order Logic Meets real-world Explainable Symbolic reasoning), the first real-world benchmark for higher-order symbolic reasoning in LLMs, containing 1379 instances. Built on higher-order logic, HOLMES pair

Why this matters
Why now

The continuous evolution of LLMs necessitates robust evaluation methods for increasingly complex reasoning capabilities, pushing the frontier beyond first-order logic.

Why it’s important

Higher-order logical reasoning is crucial for AI reliability and enables LLMs to tackle more sophisticated, real-world problems that require understanding rules and constraints.

What changes

The introduction of HOLMES provides a new benchmark, shifting the focus of LLM development and evaluation towards more advanced symbolic reasoning, impacting future AI capabilities.

Winners
  • · AI research institutions
  • · LLM developers
  • · Developers of AI safety tools
Losers
  • · LLMs with poor higher-order reasoning
  • · AI applications requiring complex logic without robust foundational models
Second-order effects
Direct

This benchmark will drive significant improvements in LLM capacity for higher-order logical reasoning.

Second

Improved logical reasoning in LLMs will unlock new applications in fields requiring complex decision-making and rule-based systems.

Third

Enhanced AI reasoning capabilities could accelerate automation in white-collar sectors and potentially lead to more reliable autonomous agents.

Editorial confidence: 90 / 100 · Structural impact: 60 / 100
Original report

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