What question did this study set out to answer?

The research aims to explore the limits of metaphysical reduction in polynomial S5 semantics and what information can be distinguished in this formalism.

August 5, 2026Open Access

What Elimination Leaves Behind: Definability and the Limits of Metaphysical Reduction in Polynomial S5 Semantics

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The research aims to explore the limits of metaphysical reduction in polynomial S5 semantics and what information can be distinguished in this formalism.
Examined polynomial ring semantics for finite S5 alongside Kripke semantics.
Analyzed the decomposition of admissible valuations into categorical assignments and definable profiles.
Studied Boolean subalgebras and their implications for possible reduction bases.
Every admissible valuation can be decomposed into categorical assignments and definable profiles.
Polynomial coordinates can be eliminated without losing definable profiles.
Exact support bounds quantify remaining modal variation in the system.

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Implication

Randomized trial investigates limitations of modal semantics in polynomial frameworks, highlighting implications for metaphysical reduction.

Cite This Study

Lorand Bruhacs (2026) studied this question.

synapsesocial.com/papers/6a72e816226790f3706579ac https://doi.org/10.5281/zenodo.21780358

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Implication

Randomized trial investigates limitations of modal semantics in polynomial frameworks, highlighting implications for metaphysical reduction.

What Elimination Leaves Behind: Definability and the Limits of Metaphysical Reduction in Polynomial S5 Semantics

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Discussion

Implication

Cite This Study

What Elimination Leaves Behind: Definability and the Limits of Metaphysical Reduction in Polynomial S5 Semantics

Key Points

Discussion

Implication

Cite This Study

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