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arxiv: 2606.31883 · v1 · pith:5QWPGR7Unew · submitted 2026-06-30 · 🧮 math.LO · cs.LO

Possibly Relevant Translations

S{\o}ren Brinck Knudstorp This is my paper

Pith reviewed 2026-07-01 02:04 UTC · model grok-4.3

classification 🧮 math.LO cs.LO
keywords relevant logicsmodal logicstranslationsstructural connectionsnormal modal logicslogic embeddings
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The pith

Translations from relevant logics into normal modal logics reveal structural connections between the two.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops translations from relevant logics into normal modal logics. These translations are then applied to clarify structural connections between relevant and modal logic. The work also produces several corollary results and identifies open questions for further study. A sympathetic reader would care because the mappings offer a way to relate two families of non-classical logics through explicit embeddings.

Core claim

We develop translations from relevant logics into normal modal logics, and use them to clarify structural connections between relevant and modal logic, obtain a few corollary results, and raise questions for future work.

What carries the argument

Translations from relevant logics into normal modal logics that preserve enough structure to map one into the other.

Load-bearing premise

The developed translations preserve enough structure to establish the claimed connections between the logics without introducing artifacts that invalidate the corollaries.

What would settle it

A relevant logic formula whose image under the translation fails to preserve validity or produces an unintended connection that contradicts known properties of the target modal logic.

Figures

Figures reproduced from arXiv: 2606.31883 by S{\o}ren Brinck Knudstorp.

Figure 1
Figure 1. Figure 1: Arrows indicate strict inclusion ⊊. Additionally, TWJ+ ̸⊆ RW+ ̸⊆ E +. To situate the relevant family within a bigger logical realm, let us note that the {∧,∨,→}-fragment of intuitionistic propositional logic IPL results from adding to R + the axiom schema ϕ → (ψ → ϕ). 3 If one further adds Peirce’s law ((ϕ → ψ) → ϕ) → ϕ, one gets the {∧,∨,→}-fragment of classical propo￾sitional logic CPL; in fact, over R +… view at source ↗
read the original abstract

We develop translations from relevant logics into normal modal logics, and use them to clarify structural connections between relevant and modal logic, obtain a few corollary results, and raise questions for future work.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript develops translations from relevant logics into normal modal logics. These translations are used to clarify structural connections between relevant and modal logic, obtain a few corollary results, and raise questions for future work.

Significance. If the translations are faithful embeddings that preserve key structural features without introducing artifacts, the work could provide a useful bridge between relevant logics and the well-developed theory of normal modal logics, potentially enabling transfer of results and new corollaries. However, the absence of any definitions, proofs, or specific statements of the translations and corollaries in the provided text prevents any concrete assessment of whether these connections are established.

major comments (2)
  1. [Abstract] Abstract: The central claim is that translations have been developed and used to obtain corollaries, but no definitions of the translations, no statements of the corollaries, and no supporting arguments or proofs are supplied. This makes it impossible to verify whether the translations preserve enough structure to support the claimed connections (cf. reader's weakest_assumption).
  2. No sections, equations, or tables are present in the available manuscript text, so no load-bearing technical claims can be examined for internal consistency or correctness.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their report. We acknowledge that the manuscript text provided consists only of the abstract, which prevents examination of the technical content and explains the concerns raised about missing definitions, proofs, and structure.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim is that translations have been developed and used to obtain corollaries, but no definitions of the translations, no statements of the corollaries, and no supporting arguments or proofs are supplied. This makes it impossible to verify whether the translations preserve enough structure to support the claimed connections (cf. reader's weakest_assumption).

    Authors: We agree that the abstract alone does not supply the definitions of the translations, the statements of the corollaries, or the supporting arguments. The current submission appears to contain only the abstract, making verification impossible at this stage. In the revised version we will include the full development of the translations, the corollary statements, and the arguments establishing the structural connections. revision: yes

  2. Referee: [—] No sections, equations, or tables are present in the available manuscript text, so no load-bearing technical claims can be examined for internal consistency or correctness.

    Authors: This observation is accurate for the text as provided. The full manuscript will contain the necessary sections, equations, and any supporting tables to present and verify the technical claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity; constructive development of translations

full rationale

The paper's central activity is the explicit construction of translations from relevant logics into normal modal logics, followed by their application to derive structural connections and corollaries. No equations, definitions, or results are shown to reduce by construction to fitted parameters, self-referential definitions, or load-bearing self-citations. The work is framed as producing new embeddings rather than predicting or deriving from prior fitted inputs, and the abstract provides no indication that any claimed connection is presupposed in the translation definitions themselves. This is the standard case of a self-contained constructive result in logic.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No details on free parameters, axioms, or invented entities are present in the abstract.

pith-pipeline@v0.9.1-grok · 5531 in / 862 out tokens · 33163 ms · 2026-07-01T02:04:50.990601+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

30 extracted references · 22 canonical work pages · 1 internal anchor

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