Notre Dame Journal of Formal Logic 57 (4):523-549 (2016)

We characterize all finitary consequence relations over S4.3, both syntactically, by exhibiting so-called passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic L extending S4 has projective unification if and only if L contains S4.3. In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the known results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relations over S4.3 is countable and distributive and it forms a Heyting algebra.
Keywords $\mathbf{S4.3}$   consequence relations   projective unification   quasivarieties   structural completeness  admissible rules
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DOI 10.1215/00294527-3636512
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References found in this work BETA

Unification in Modal and Description Logics.Franz Baader & Silvio Ghilardi - 2011 - Logic Journal of the IGPL 19 (6):705-730.
Extensions of the Lewis System S5.Schiller Joe Scroggs - 1951 - Journal of Symbolic Logic 16 (2):112-120.
The Logics Containing S 4.3.Kit Fine - 1971 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):371-376.
That All Normal Extensions of S4.3 Have the Finite Model Property.R. A. Bull - 1966 - Mathematical Logic Quarterly 12 (1):341-344.

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Citations of this work BETA

Almost Structural Completeness; an Algebraic Approach.Wojciech Dzik & Michał M. Stronkowski - 2016 - Annals of Pure and Applied Logic 167 (7):525-556.

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