Modal logic with names

Journal of Philosophical Logic 22 (6):607 - 636 (1993)
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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DOI 10.1007/BF01054038
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References found in this work BETA
Krister Segerberg (1971). An Essay in Classical Modal Logic. Uppsala,Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
Patrick Blackburn (1992). Nominal Tense Logic. Notre Dame Journal of Formal Logic 34 (1):56-83.

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Citations of this work BETA
Patrick Blackburn & Jerry Seligman (1995). Hybrid Languages. Journal of Logic, Language and Information 4 (3):251-272.
Stefan Wölfl (2002). Propositional Q-Logic. Journal of Philosophical Logic 31 (5):387-414.

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