Journal of Philosophical Logic

, Volume 22, Issue 6, pp 607–636 | Cite as

Modal logic with names

  • George Gargov
  • Valentin Goranko
Article

Abstract

We investigate an enrichment of the propositional modal language with a “universal” modality ▪ having semanticsx ⊧ ▪ϕ iff āy(y ⊧ ϕ), and a countable set of “names” — a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒc proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(
) of, where
is an additional modality with the semanticsx ⊧
ϕ iff āy(y⊧ x → y ⊧ϕ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒc. Strong completeness of the normal ℒc-logics is proved with respect to models in which all worlds are named. Every ℒc-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 to ℒcare discussed. Finally, further perspectives for names in multimodal environment are briefly sketched.

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • George Gargov
    • 1
  • Valentin Goranko
    • 2
  1. 1.ShrewsburyUSA
  2. 2.Department of MathematicsUniversity of the North, QwaQwa BranchPhuthaditjhabaRepublic of South Africa

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