Same Formulas, Different Semantics: Do Language Models Follow Modal Logic Specifications?

Noosaga Placements

• Natural Language Processingsubfield95%
  The paper evaluates language models on natural language reasoning tasks, focusing on their ability to follow semantic specifications in modal logic, which is a core NLP evaluation concern.
  Evaluating language models on such problems requires testing whether their judgments follow the stated semantics rather than a familiar logic.Most NLP reasoning benchmarks instead assume a fixed background logic and vary the facts, rules, or proof depth.
• Large Language Modelsframework95%
  The paper directly evaluates several large language models (DeepSeek V4 Flash/Pro, GPT-5.6 Luna/Terra, Claude Sonnet 5) on the proposed benchmark.
  We evaluate dated endpoints for DeepSeek V4 Flash and Pro, GPT-5.6 Luna and Terra, and Claude Sonnet 5.On this core, four of five recent models perform below the condition-only baseline under direct prompting.
• Formal Semantics and Logic-Based Approachesframework90%
  The paper is situated within formal semantics and logic-based approaches to NLP, as it evaluates models on modal logic specifications and uses automated theorem proving as an oracle.
  We use that formal infrastructure as an oracle rather than proposing a new logic or prover.Our diagnostic tests whether models follow modal specifications by holding the linguistic problem fixed, changing one declared model-theoretic condition.
• Knowledge Representation Reasoningsubfield80%
  The paper deals with formal semantics of modal logic, Kripke frames, and domain conditions, which are central to knowledge representation and reasoning about necessity and possibility.
  Reasoning about necessity and possibility depends on assumptions about accessibility between worlds and about which objects exist at each one.We use the familiar systems K, D, T, B, S4, and S5, while storing their explicit frame properties.
• Symbolic NLPframework70%
  The paper compares different representations (named English, relational definitions, TPTP) and contrasts symbolic formal logic with neural model behavior.
  Representation is not a simple fix. The matched pilot also argues against a purely surface-level explanation.Formal syntax changes which errors appear without removing the need to follow the stipulated model class.
• Computational Linguisticssubfield60%
  The paper uses controlled English renderings of modal logic problems and evaluates how language models interpret natural language specifications, which touches on computational linguistics.
  The renderer is deterministic and directly states the relevant semantics.Prompts spell out rules but withhold conventional system names.

Abstract

Reasoning about necessity and possibility depends on assumptions about accessibility between worlds and about which objects exist at each one. The same inference may therefore hold under one modal system and fail under another. Evaluating language models on such problems requires testing whether their judgments follow the stated semantics rather than a familiar logic. We construct paired modal problems with identical premises and conjecture but different frame or domain conditions; automated reasoning verifies opposite labels. A balanced core prevents the semantic condition alone from revealing the answer. On this core, four of five recent models perform below the condition-only baseline under direct prompting. Yet enabling reasoning mode raises DeepSeek V4 Flash from 4.4% to 88.1% on unchanged prompts. Following stipulated modal semantics thus depends strongly on inference mode as well as model identity. When frame conditions are omitted, models often agree but fit different familiar logics best. We release the formulas, oracle artifacts, countermodels, and responses.

Paper Context