9 found
Sort by:
  1. Balder ten Cate & Jan van Eijck, Expressivity of Extensions of Dynamic First-Order Logic.
    Dynamic predicate logic (DPL), presented in [5] as a formalism for representing anaphoric linking in natural language, can be viewed as a fragment of a well known formalism for reasoning about imperative programming [6]. An interesting difference from other forms of dynamic logic is that the distinction between formulas and programs gets dropped: DPL formulas can be viewed as programs. In this paper we show that DPL is in fact the basis of a hierarchy of formulas-as-programs languages.
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  2. Balder ten Cate & Jan van Eijck, Expressivity of Extensions of Dynamic First-Order Logic.
    Dynamic predicate logic (DPL), presented in [5] as a formalism for representing anaphoric linking in natural language, can be viewed as a fragment of a well known formalism for reasoning about imperative programming [6]. An interesting difference from other forms of dynamic logic is that the distinction between formulas and programs gets dropped: DPL formulas can be viewed as programs. In this paper we show that DPL is in fact the basis of a hierarchy of formulas-as-programs languages.
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  3. Balder ten Cate, Gaëlle Fontaine & Tadeusz Litak (2010). Some Modal Aspects of XPath. Journal of Applied Non-Classical Logics 20 (3):139-171.
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  4. Balder Ten Cate, David Gabelaia & Dmitry Sustretov (2009). Modal Languages for Topology: Expressivity and Definability. Annals of Pure and Applied Logic 159 (1):146-170.
    In this paper we study the expressive power and definability for modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt–Thomason definability theorem in terms of the well-established first-order topological language.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  5. Patrick Blackburn & Balder Ten Cate (2006). Pure Extensions, Proof Rules, and Hybrid Axiomatics. Studia Logica 84 (2):277-322.
    In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language to the strong Priorean language . We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  6. Balder ten Cate (2006). Expressivity of Second Order Propositional Modal Logic. Journal of Philosophical Logic 35 (2):209-223.
    We consider second-order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem–Rosen theorem and the Goldblatt Thomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of SOPML, and we characterize the bounded fragment of first-order logic as being the intersection of first-order logic and SOPML.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  7. Johan van Benthem, Guram Bezhanishvili, Balder ten Cate & Darko Sarenac (2006). Multimo Dal Logics of Products of Topologies. Studia Logica 84 (3):369-392.
    We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion ${\bf S4}\oplus {\bf S4}$ . We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers ${\Bbb Q}\times {\Bbb Q}$ (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  8. Balder ten Cate (2005). Interpolation for Extended Modal Languages. Journal of Symbolic Logic 70 (1):223-234.
    Several extensions of the basic modal language are characterized in terms of interpolation. Our main results are of the following form: Language ℒ' is the least expressive extension of ℒ with interpolation. For instance, let ℳ be the extension of the basic modal language with a difference operator [7]. First-order logic is the least expressive extension of ℳ with interpolation. These characterizations are subsequently used to derive new results about hybrid logic, relation algebra and the guarded fragment.
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  9. Balder ten Cate & Massimo Franceschet (2005). Guarded Fragments with Constants. Journal of Logic 14 (3):281-288.
    We prove ExpTime-membership of the satisfiability problem for loosely ∀-guarded first-order formulas with a bounded number of variables and an unbounded number of constants. Guarded fragments with constants are interesting by themselves and because of their connection to hybrid logic.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation