Switch to: References

Add citations

You must login to add citations.
  1. Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.
    This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic. In addition, the book discusses a broad range of topics, including standard modal logic results ; bisimulations for neighborhood models and other model-theoretic (...)
    $36.09 new    View on Amazon.com
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   33 citations  
  • Some descending chains of incomplete modal logics.Ming Xu - 1991 - Journal of Philosophical Logic 20 (3):265 - 283.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Topology and duality in modal logic.Giovanni Sambin & Virginia Vaccaro - 1988 - Annals of Pure and Applied Logic 37 (3):249-296.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   28 citations  
  • Incompleteness and Fixed Points.Lorenzo Sacchetti - 2002 - Mathematical Logic Quarterly 48 (1):15-28.
    Our purpose is to present some connections between modal incompleteness andmodal logics related to the Gödel-Löb logic GL. One of our goals is to prove that for all m, n, k, l ∈ ℕ the logic K + equation image□i □jp ↔ p) → equation image□ip is incomplete and does not have the fixed point property. As a consequence we shall obtain that the Boolos logic KH does not have the fixed point property.
    Direct download  
     
    Export citation  
     
    Bookmark  
    		•
  • Kripke Incomplete Logics Containing KTB.Yutaka Miyazaki - 2007 - Studia Logica 85 (3):303-317.
    It is shown that there is a Kripke incomplete logic in NExt(KTB ⊕ □2 p → □3 p). Furthermore, it is also shown that there exists a continuum of Kripke incomplete logics in NExt(KTB ⊕ □5 p → □6 p).
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • Complete additivity and modal incompleteness.Wesley H. Holliday & Tadeusz Litak - 2019 - Review of Symbolic Logic 12 (3):487-535.
    In this article, we tell a story about incompleteness in modal logic. The story weaves together an article of van Benthem, “Syntactic aspects of modal incompleteness theorems,” and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, ${\cal V}$-baos. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem’s article resolves the open question (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  • Elementary canonical formulae: extending Sahlqvist’s theorem.Valentin Goranko & Dimiter Vakarelov - 2006 - Annals of Pure and Applied Logic 141 (1):180-217.
    We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   26 citations  
  • Mathematical modal logic: A view of its evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   53 citations  
  • Magari's theorem via the recession frame.M. J. Cresswell - 1987 - Journal of Philosophical Logic 16 (1):13 - 15.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • A simple incomplete extension of T which is the union of two complete modal logics with F.m.P.Roy A. Benton - 2002 - Journal of Philosophical Logic 31 (6):527-541.
    I present here a modal extension of T called KTLM which is, by several measures, the simplest modal extension of T yet presented. Its axiom uses only one sentence letter and has a modal depth of 2. Furthermore, KTLM can be realized as the logical union of two logics KM and KTL which each have the finite model property (f.m.p.), and so themselves are complete. Each of these two component logics has independent interest as well.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations