Generalized Explosion Principles: A Semantic Perspective

Sankha S. Basu; Sayantan Roy

arxiv: 2511.00912 · v2 · submitted 2025-11-02 · 🧮 math.LO

Generalized Explosion Principles: A Semantic Perspective

Sankha S. Basu , Sayantan Roy This is my paper

Pith reviewed 2026-05-18 01:17 UTC · model grok-4.3

classification 🧮 math.LO

keywords explosion principlesabstract model structuressatisfiabilityunsatisfiabilitysemantic logicparaconsistent logiclogical principles

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The pith

Semantic analogues of explosion principles are defined and interconnected using abstract model structures and unsatisfiability.

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

The paper establishes a semantic treatment of logical explosion principles, where an inconsistent set of assumptions forces every statement to hold, by working in abstract model structures that track satisfiability and finite satisfiability. It formulates several such principles directly in terms of unsatisfiability or finite unsatisfiability and introduces semantic versions of principles previously given in the literature. These definitions allow the paper to characterize the new principles and map out their logical interconnections. A reader would care because the separation of semantic from syntactic notions opens the possibility of studying explosion behavior independently of any particular proof system.

Core claim

Various principles of explosion can be described in terms of unsatisfiability or finite unsatisfiability within abstract model structures; the semantic analogues of earlier syntactic principles are included among them, and the paper provides characterizations together with the interconnections that hold between all of these principles.

What carries the argument

Abstract model structures that supply independent notions of satisfiability and finite satisfiability, thereby supporting semantic explosion principles defined solely in terms of which sets of sentences are (finitely) unsatisfiable.

If this is right

Explosion principles become available for analysis in logics that lack a complete proof system or where syntactic and semantic notions diverge.
Finite unsatisfiability yields a distinct family of explosion principles that may hold in structures where ordinary unsatisfiability does not.
The interconnections supply a partial order or hierarchy among the semantic principles that can be checked directly in any given model structure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same semantic framework could be used to define controlled forms of explosion suitable for paraconsistent reasoning without changing the underlying syntax.
Results about these principles might transfer to other semantic notions such as entailment or consistency preservation across different model classes.
The approach suggests a route for comparing explosion behavior in classical versus non-classical semantics by varying only the model structures.

Load-bearing premise

It is possible to define abstract model structures so that semantic notions of satisfiability stand apart from any syntactic derivation rules.

What would settle it

An explicit abstract model structure in which the proposed semantic explosion principles either fail to satisfy the claimed characterizations or exhibit different interconnections from those stated.

Figures

Figures reproduced from arXiv: 2511.00912 by Sankha S. Basu, Sayantan Roy.

**Figure 1.** Figure 1: Semantic explosion principles - the sat variants The rest of this subsection is aimed at showing that no other implication holds between these principles of explosion. To begin with, we first show that sECQ-sat does not imply gECQ-sat. Example 3.7 (sECQ-sat ≠⇒ gECQ-sat). Let M = (M, |=,P(L)) be an amst, where |= M× P(L) is defined as follows. For all m ∈ M and Γ ⊆ L, m |= Γ iff Γ is finite. Then, as L is … view at source ↗

**Figure 2.** Figure 2: Semantic explosion principles - the sat variants The intended interpretation of the figure is the same as [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗

**Figure 3.** Figure 3: Semantic Explosion 21 [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗

read the original abstract

This article is motivated by the fact that there is a distinction between the descriptions of logical explosion from syntactic and semantic points of view. The discussion is illustrated using the concept of abstract model structures and the notions of satisfiability and finite satisfiability in these structures. Various principles of explosion have been described in terms of unsatisfiability or finite unsatisfiability. The semantic analogues of the principles of explosion introduced in [3] have also been considered among these. The article also studies the characterizations of and the interconnections between these new principles of explosion.

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.

Desk Editor's Note private letter to a colleague

The paper defines semantic versions of explosion principles through unsatisfiability in abstract model structures and maps their interconnections with the syntactic principles from the authors' earlier work.

read the letter

The core contribution is a set of semantic explosion principles defined directly in terms of unsatisfiability and finite unsatisfiability inside abstract model structures. The authors then characterize these principles and trace how they relate to one another and to the syntactic versions introduced in their prior paper [3]. The separation between semantic satisfaction and syntactic derivation is maintained throughout, which is the main technical point of using abstract models here. That separation looks deliberate and consistent on the basis of the abstract and the stress-test note, and the claimed characterizations appear to follow from the definitions without obvious circularity or hidden syntactic assumptions. This is a straightforward and useful extension of the earlier syntactic treatment rather than a rehash. The work stays tightly focused, which keeps the claims manageable but also limits the reach. The results will mainly interest people already working on explosion principles or on model-theoretic approaches to paraconsistent logics. A reader who has followed the syntactic side in [3] will see the natural duals and the interconnections they produce. The paper does not claim to reorganize larger parts of logic or model theory, and the specialized framing means it will not be central for most readers. Still, the program is coherent and the distinctions are checkable once the proofs are in hand. It deserves a serious referee because the setup is clean enough that referees can verify the characterizations and interconnections directly. I would send it out for review.

Referee Report

1 major / 3 minor

Summary. The paper develops a semantic treatment of generalized explosion principles within abstract model structures, defining them via (finite) unsatisfiability. It introduces semantic analogues of the explosion principles from [3], provides characterizations of these principles, and examines their interconnections.

Significance. If the characterizations and interconnections are established without syntactic leakage, the work supplies a model-theoretic separation between semantic and syntactic notions of explosion. This framework could clarify distinctions in non-classical logics (e.g., paraconsistent systems) where explosion fails, and the generality of abstract model structures is a positive feature for broader applicability.

major comments (1)

The central claim that the semantic principles are formally distinct from their syntactic counterparts (and from those in [3]) requires an explicit demonstration that the satisfaction relation in the abstract model structures is independent of any derivability relation; this should be verified in the section defining the semantic analogues.

minor comments (3)

The abstract is concise but could briefly indicate the main theorems or key characterizations obtained.
Notation for satisfiability and finite satisfiability should be introduced with a dedicated definition early in the paper to aid readability.
Ensure that all interconnections between the new semantic principles are summarized in a table or diagram for clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the helpful suggestion to strengthen the presentation of the central distinction between semantic and syntactic explosion principles. We address the major comment below and have incorporated a clarifying revision.

read point-by-point responses

Referee: The central claim that the semantic principles are formally distinct from their syntactic counterparts (and from those in [3]) requires an explicit demonstration that the satisfaction relation in the abstract model structures is independent of any derivability relation; this should be verified in the section defining the semantic analogues.

Authors: We agree that an explicit statement of this independence improves clarity. Abstract model structures are introduced in the paper as purely semantic entities whose satisfaction relation is defined model-theoretically via the interpretation of formulas in structures, without any reference to a consequence relation, derivability, or syntactic rules. In the section defining the semantic analogues, unsatisfiability is therefore taken directly from the model-theoretic notion. To make this independence fully explicit as requested, we have added a short clarifying paragraph immediately after the definition of the semantic explosion principles, stating that the satisfaction relation does not presuppose or depend upon any derivability relation and is thus independent of the syntactic principles studied in [3]. This addition confirms the formal separation without altering the technical content. revision: yes

Circularity Check

0 steps flagged

Minor self-citation to syntactic precursors; new semantic definitions remain independent

full rationale

The paper defines semantic explosion principles directly in terms of unsatisfiability and finite unsatisfiability within abstract model structures, which by design separate semantic satisfaction from syntactic derivability. It then characterizes interconnections among these new principles and their analogues from the cited syntactic work [3]. No equation or central claim reduces by construction to a fitted parameter, self-redefinition, or load-bearing self-citation chain; the abstract model structure framework supplies the required independence, rendering the derivation self-contained against external semantic benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard background assumptions of model theory and abstract model structures; no free parameters or invented entities are evident from the abstract.

axioms (1)

domain assumption Abstract model structures exist and support well-defined notions of satisfiability and finite satisfiability that are independent of syntactic derivations.
The entire semantic treatment of explosion principles rests on this modeling choice.

pith-pipeline@v0.9.0 · 5608 in / 1207 out tokens · 42069 ms · 2026-05-18T01:17:56.317649+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

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work page arXiv 2025

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S. S. Basu and E. Jain,Paracomplete probabilities,https://arxiv.org/abs/2507.04312 (2025), 18 pages. 6, 7

work page arXiv 2025

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S. S. Basu and S. Roy,Negation-free definitions of paraconsistency, Proceedings of the 10th International Conference on Non-Classical Logics. Theory and Applications, L´ od´ z, Poland, 14- 18 March 2022 (Andrzej Indrzejczak and Micha l Zawidzki, eds.), Electronic Proceedings in Theoretical Computer Science, vol. 358, Open Publishing Association, 2022, pp....

work page 2022

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An International Journal for Symbolic Logic113(2025), no

,Generalized explosion principles, Studia Logica. An International Journal for Symbolic Logic113(2025), no. 4, 1025–1060. 1, 2, 3, 7, 8, 22

work page 2025

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B´ eziau,Universal logic, Logica’94 - Proceedings of the 8th International Symposium (Prague) (T.Childers and O.Majer, eds.), 1994, pp

J.-Y. B´ eziau,Universal logic, Logica’94 - Proceedings of the 8th International Symposium (Prague) (T.Childers and O.Majer, eds.), 1994, pp. 73–93. 2 22

work page 1994

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Department of Logic

,13 questions about universal logic, University of L´ od´ z. Department of Logic. Bulletin of the Section of Logic35(2006), no. 2-3, 133–150, Questions by Linda Eastwood. 2

work page 2006

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Priest,An introduction to non-classical logic, Cambridge University Press, Cambridge, 2001

G. Priest,An introduction to non-classical logic, Cambridge University Press, Cambridge, 2001. 2

work page 2001

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S. Roy, S. S. Basu, and M. K. Chakraborty,Abstract model structures and compactness theorems, https://arxiv.org/abs/2507.02343(2025), 33 pages. 2, 3, 4, 6, 22 23

work page arXiv 2025