Modal logic with names

Journal of Philosophical Logic 22 (6):607 - 636 (1993)
Abstract
We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched
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    References found in this work BETA
    Patrick Blackburn (1992). Nominal Tense Logic. Notre Dame Journal of Formal Logic 34 (1):56-83.
    John P. Burgess (1982). Axioms for Tense Logic. II. Time Periods. Notre Dame Journal of Formal Logic 23 (4):375-383.
    Valentin Goranko (1989). Modal Definability in Enriched Languages. Notre Dame Journal of Formal Logic 31 (1):81-105.

    View all 10 references

    Citations of this work BETA
    M. J. Cresswell (2010). Temporal Reference in Linear Tense Logic. Journal of Philosophical Logic 39 (2):173 - 200.
    Dmitry Sustretov (2009). Hybrid Logics of Separation Axioms. Journal of Logic, Language and Information 18 (4):541-558.

    View all 11 citations

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