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    The translation preserves the deductive structure of S4 — Carmelics
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    Supports→Modal logic S4 is deductively embeddable into many-sorted logic: if Π ⊢_S4 φ then Trans(Π) ∪ ΔS4 ⊢ Trans(φ).

    The translation preserves the deductive structure of S4

    Modality & PossibilityProof of definition segments
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    Modal logic S4 is deductively embeddable into many-sorted logic: if Π ⊢_S4 φ the...Translations of axioms T and 4 are theorems of ΔS4

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    Given a Kripke structure \[\mathcal{A}=\langle \mathbf{W},\mathbf{R},\langle P^{\mathcal{A}}\rangle _{P\in \Atom}\rangle\] we say that \(\mathcal{AG}\) is a general structure built on \(\mathcal{A}\) if and only if \[\mathcal{AG}=\langle \mathbf{W},\mathbf{W}^{\prime },\mathbf{R},\epsilon _{1}^{\mathcal{A}},\langle P^{\mathcal{A}}\rangle _{P\in \Atom}\rangle\] where \(\Def \subseteq \mathbf{W}^{\prime }\subseteq \wp (\mathbf{W})\). [22] It can be proved that the set of worlds where a moda

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