Non-Deterministic Many-Valued Modal Logic

Ferguson, Thomas Macaulay

doi:10.1109/ismvl52857.2022.00023

2022 IEEE 52nd International Symposium on Multiple-Valued Logic (ISMVL) 2022

DOI: 10.1109/ismvl52857.2022.00023

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Non-Deterministic Many-Valued Modal Logic

Thomas Macaulay Ferguson

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2024

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A Gödel-Dugundji-style theorem for the minimal structural logic

Pawlowski,

Ferguson,

Gertler

2024

Journal of Logic and Computation

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This paper introduces a sequent calculus, $\textbf{M}_{\textbf{S}}$, the minimal structural logic, which includes all structural rules while excluding operational ones. Despite its limited calculus, $\textbf{M}_{\textbf{S}}$ unexpectedly shares a property with intuitionistic logic and modal logics between $\textsf{S1}$ and $\textsf{S5}$: it lacks sound and complete finitely-valued (deterministic) semantics. Mirroring Gödel’s and Dugundji’s findings, we demonstrate that $\textbf{M}_{\textbf{S}}$ does possess a natural finitely-valued non-deterministic semantics. In fact, we show that $\textbf{M}_{\textbf{S}}$ is sound and complete with respect to any semantics belonging to a natural class of maximally permissive non-deterministic matrices. We close by examining the case of subsystems of $\textbf{M}_{\textbf{S}}$, including the “structural kernels” of the strict-tolerant and tolerant-strict logics $\textbf{ST}$ and $\textbf{TS}$, and strengthen this result to also preclude finitely-valued deterministic semantics with respect to variable designated value frameworks.

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A Gödel-Dugundji-style theorem for the minimal structural logic

Pawlowski,

Ferguson,

Gertler

2024

Journal of Logic and Computation

View full text Add to dashboard Cite

show abstract

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Non-Deterministic Many-Valued Modal Logic

Cited by 1 publication

References 13 publications

A Gödel-Dugundji-style theorem for the minimal structural logic

A Gödel-Dugundji-style theorem for the minimal structural logic

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