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The aim is to investigate the modal closure and symmetry characteristics of finite S5 supervenience lattices.

August 6, 2026Open Access

Which Base? Modal Closure and Symmetry in the Finite S5 Supervenience Lattice

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The aim is to investigate the modal closure and symmetry characteristics of finite S5 supervenience lattices.
Analyzed the subalgebra lattice of modal proposition algebra for finite S5.
Computed the automorphism group of the finite S5 profile algebra.
Established criteria for modal closure and examined categorical bases.
Identified that the cluster base is fixed pointwise under necessity while the categorical base is not closed.
Showed that restoring internal Boolean-lattice order minimizes symmetries to propositional dimensions.
Classified characteristic bases, proving that all are modally closed.

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Examines modal closure and symmetry in finite propositional S5, highlighting implications for categorical bases.

Lorand Bruhacs (2026) studied this question.

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