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Representation Theorems for Cumulative Propositional Dependence Logics

Juha Kontinen, Arne Meier, Kai Sauerwald · Feb 24, 2026 · Citations: 0

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Data freshness

Extraction: Fresh

Check recency before relying on this page for active eval decisions. Use stale pages as context and verify against current hub results.

Metadata refreshed

Feb 24, 2026, 8:45 PM

Stale

Extraction refreshed

Apr 12, 2026, 10:37 PM

Fresh

Extraction source

Persisted extraction

Confidence 0.15

Abstract

This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics. Cumulative logics are famously given by System C. For propositional dependence logic, we show that System C entailments are exactly captured by cumulative models from Kraus, Lehmann and Magidor. On the other hand, we show that entailment in cumulative propositional logics with team semantics is exactly captured by cumulative and asymmetric models. For the latter, we also obtain equivalence with cumulative logics based on propositional logic with classical semantics. The proofs will be useful for proving representation theorems for other cumulative logics without negation and material implication.

Low-signal caution for protocol decisions

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  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.15 (below strong-reference threshold).
  • No explicit evaluation mode was extracted from available metadata.
  • No benchmark/dataset or metric anchors were extracted.
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HFEPX Relevance Assessment

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

Background context only.

Main weakness

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit Score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

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Field Provenance & Confidence

Each key protocol field shows extraction state, confidence band, and data source so you can decide whether to trust it directly or validate from full text.

Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

No explicit feedback protocol extracted.

Evidence snippet: This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics.

Evaluation Modes

missing

None explicit

Confidence: Low Source: Persisted extraction missing

Validate eval design from full paper text.

Evidence snippet: This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics.

Quality Controls

missing

Not reported

Confidence: Low Source: Persisted extraction missing

No explicit QC controls found.

Evidence snippet: This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics.

Benchmarks / Datasets

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No benchmark anchors detected.

Evidence snippet: This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics.

Reported Metrics

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No metric anchors detected.

Evidence snippet: This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics.

Rater Population

missing

Unknown

Confidence: Low Source: Persisted extraction missing

Rater source not explicitly reported.

Evidence snippet: This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: Math
  • Extraction source: Persisted extraction

Evaluation Lens

  • Evaluation modes:
  • Agentic eval: None
  • Quality controls: Not reported
  • Confidence: 0.15
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Deterministic synthesis

For propositional dependence logic, we show that System C entailments are exactly captured by cumulative models from Kraus, Lehmann and Magidor. HFEPX protocol signal is limited in abstract-level metadata, so treat it as adjacent context. Updated from current HFEPX corpus.

Generated Apr 12, 2026, 10:37 PM · Grounded in abstract + metadata only

Key Takeaways

  • For propositional dependence logic, we show that System C entailments are exactly captured by cumulative models from Kraus, Lehmann and Magidor.
  • On the other hand, we show that entailment in cumulative propositional logics with team semantics is exactly captured by cumulative and asymmetric models.
  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Actions

  • Treat this as method context, then pivot to protocol-specific HFEPX hubs.
  • Identify benchmark choices from full text before operationalizing conclusions.
  • Verify metric definitions before comparing against your eval pipeline.

Caveats

  • Generated from title, abstract, and extracted metadata only; full-paper implementation details are not parsed.
  • Low-signal flag detected: protocol relevance may be indirect.

Research Summary

Contribution Summary

  • For propositional dependence logic, we show that System C entailments are exactly captured by cumulative models from Kraus, Lehmann and Magidor.
  • On the other hand, we show that entailment in cumulative propositional logics with team semantics is exactly captured by cumulative and asymmetric models.

Why It Matters For Eval

  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Gap: Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Gap: Metric reporting is present

    No metric terms extracted.

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