32 found
Sort by:
  1. Frank Wolter (2014). The Algebraic Face of Minimality. Logic and Logical Philosophy 6:225.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  2. Mikhail Sheremet, Frank Wolter & Michael Zakharyaschev (2010). A Modal Logic Framework for Reasoning About Comparative Distances and Topology. Annals of Pure and Applied Logic 161 (4):534-559.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  3. Hans Tompits, Ken Satoh, Arnold Beckmann, Carlos Caleiro, Thomas Eiter, Sylvain Salvati, Taisuke Sato & Frank Wolter (2010). 16th Workshop on Logic, Language, Information and Computation (WoLLIC 2009). Bulletin of Symbolic Logic 16 (1).
    Direct download  
     
    My bibliography  
     
    Export citation  
  4. Patrick Blackburn, Johan van Benthem & Frank Wolter (eds.) (2007). Handbook of Modal Logic. Elsevier.
    The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners (...)
    Direct download  
     
    My bibliography  
     
    Export citation  
  5. David Gabelaia, Agi Kurucz, Frank Wolter & Michael Zakharyaschev (2006). Non-Primitive Recursive Decidability of Products of Modal Logics with Expanding Domains. Annals of Pure and Applied Logic 142 (1):245-268.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  6. David Gabelaia, Agi Kurucz, Frank Wolter & Michael Zakharyaschev (2005). Products of 'Transitive' Modal Logics. Journal of Symbolic Logic 70 (3):993-1021.
    We solve a major open problem concerning algorithmic properties of products of ‘transitive’ modal logics by showing that products and commutators of such standard logics as K4, S4, S4.1, K4.3, GL, or Grz are undecidable and do not have the finite model property. More generally, we prove that no Kripke complete extension of the commutator [K4,K4] with product frames of arbitrary finite or infinite depth (with respect to both accessibility relations) can be decidable. In particular, if.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  7. Tadeusz Litak & Frank Wolter (2005). All Finitely Axiomatizable Tense Logics of Linear Time Flows Are CoNP-Complete. Studia Logica 81 (2):153 - 165.
    We prove that all finitely axiomatizable tense logics with temporal operators for ‘always in the future’ and ‘always in the past’ and determined by linear fows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form ■n+1F p → nF p, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all ∩-irreducible tense logics. As these classes of tense logics contain many Kripke incomplete bimodal logics, we obtain many natural (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  8. Frank Wolter & Michael Zakharyaschev (2005). A Logic for Metric and Topology. Journal of Symbolic Logic 70 (3):795 - 828.
    We propose a logic for reasoning about metric spaces with the induced topologies. It combines the 'qualitative' interior and closure operators with 'quantitative' operators 'somewhere in the sphere of radius r.' including or excluding the boundary. We supply the logic with both the intended metric space semantics and a natural relational semantics, and show that the latter (i) provides finite partial representations of (in general) infinite metric models and (ii) reduces the standard '∈-definitions' of closure and interior to simple constraints (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  9. Roman Kontchakov, Carsten Lutz, Frank Wolter & Michael Zakharyaschev (2004). Temporalising Tableaux. Studia Logica 76 (1):91 - 134.
    As a remedy for the bad computational behaviour of first-order temporal logic (FOTL), it has recently been proposed to restrict the application of temporal operators to formulas with at most one free variable thereby obtaining so-called monodic fragments of FOTL. In this paper, we are concerned with constructing tableau algorithms for monodic fragments based on decidable fragments of first-order logic like the two-variable fragment or the guarded fragment. We present a general framework that shows how existing decision procedures for first-order (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  10. Oliver Kutz, Holger Sturm, Nobu-Yuki Suzuki, Frank Wolter & Michael Zakharyaschev (2002). Axiomatizing Distance Logics. Journal of Applied Non-Classical Logics 12 (3-4):425-439.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  11. Carsten Lutz, Holger Sturm, Frank Wolter & Michael Zakharyaschev (2002). A Tableau Decision Algorithm for Modalized ALC with Constant Domains. Studia Logica 72 (2):199-232.
    The aim of this paper is to construct a tableau decision algorithm for the modal description logic K ALC with constant domains. More precisely, we present a tableau procedure that is capable of deciding, given an ALC-formula with extra modal operators (which are applied only to concepts and TBox axioms, but not to roles), whether is satisfiable in a model with constant domains and arbitrary accessibility relations. Tableau-based algorithms have been shown to be practical even for logics of rather high (...)
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  12. Frank Wolter & Michael Zakharyaschev (2002). Axiomatizing the Monodic Fragment of First-Order Temporal Logic. Annals of Pure and Applied Logic 118 (1-2):133-145.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  13. Holger Sturm & Frank Wolter (2001). First-Order Expressivity for S5-Models: Modal Vs. Two-Sorted Languages. Journal of Philosophical Logic 30 (6):571-591.
    Standard models for model predicate logic consist of a Kripke frame whose worlds come equipped with relational structures. Both modal and two-sorted predicate logic are natural languages for speaking about such models. In this paper we compare their expressivity. We determine a fragment of the two-sorted language for which the modal language is expressively complete on S5-models. Decidable criteria for modal definability are presented.
    Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  14. Frank Wolter & Michael Zakharyaschev (2001). Decidable Fragments of First-Order Modal Logics. Journal of Symbolic Logic 66 (3):1415-1438.
    The paper considers the set ML 1 of first-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using a mosaic technique, we prove a general satisfiability criterion for formulas in ML 1 , which reduces the modal satisfiability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragments of various modal predicate logics.
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  15. Ian Hodkinson, Frank Wolter & Michael Zakharyaschev (2000). Decidable Fragments of First-Order Temporal Logics. Annals of Pure and Applied Logic 106 (1-3):85-134.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  16. Frank Wolter (2000). First Order Common Knowledge Logics. Studia Logica 65 (2):249-271.
    In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal properties of "quantifying into" (...)
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  17. Marcus Kracht & Frank Wolter (1999). Normal Monomodal Logics Can Simulate All Others. Journal of Symbolic Logic 64 (1):99-138.
    This paper shows that non-normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  18. Yasuhito Suzuki, Frank Wolter & Michael Zakharyaschev (1998). Speaking About Transitive Frames in Propositional Languages. Journal of Logic, Language and Information 7 (3):317-339.
    This paper is a comparative study of the propositional intuitionistic (non-modal) and classical modal languages interpreted in the standard way on transitive frames. It shows that, when talking about these frames rather than conventional quasi-orders, the intuitionistic language displays some unusual features: its expressive power becomes weaker than that of the modal language, the induced consequence relation does not have a deduction theorem and is not protoalgebraic. Nevertheless, the paper develops a manageable model theory for this consequence and its extensions (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  19. Frank Wolter (1998). All Finitely Axiomatizable Subframe Logics Containing the Provability Logic CSM_{0} Are Decidable. Archive for Mathematical Logic 37 (3):167-182.
    In this paper we investigate those extensions of the bimodal provability logic ${\vec CSM}_{0}$ (alias ${\vec PRL}_{1}$ or ${\vec F}^{-})$ which are subframe logics, i.e. whose general frames are closed under a certain type of substructures. Most bimodal provability logics are in this class. The main result states that all finitely axiomatizable subframe logics containing ${\vec CSM}_{0}$ are decidable. We note that, as a rule, interesting systems in this class do not have the finite model property and are not even (...)
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  20. Frank Wolter (1998). All Finitely Axiomatizable Subframe Logics Containing the Provability Logic CS.. Archive for Mathematical Logic 37 (3).
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  21. Frank Wolter (1998). On Logics with Coimplication. Journal of Philosophical Logic 27 (4):353-387.
    This paper investigates (modal) extensions of Heyting-Brouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We first develop matrix as well as Kripke style semantics for those logics. Then, by extending the Gö;del-embedding of intuitionistic logic into S4, it is shown that all (modal) extensions of Heyting-Brouwer logic can be embedded into tense logics (with additional modal operators). An extension of the Blok-Esakia-Theorem is proved for this embedding.
    Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  22. Marcus Kracht & Frank Wolter (1997). Simulation and Transfer Results in Modal Logic – a Survey. Studia Logica 59 (2):149-177.
    This papers gives a survey of recent results about simulations of one class of modal logics by another class and of the transfer of properties of modal logics under extensions of the underlying modal language. We discuss: the transfer from normal polymodal logics to their fusions, the transfer from normal modal logics to their extensions by adding the universal modality, and the transfer from normal monomodal logics to minimal tense extensions. Likewise, we discuss simulations of normal polymodal logics by normal (...)
    Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  23. Frank Wolter (1997). A Note on the Interpolation Property in Tense Logic. Journal of Philosophical Logic 26 (5):545-551.
    It is proved that all bimodal tense logics which contain the logic of the weak orderings and have unbounded depth do not have the interpolation property.
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  24. Frank Wolter (1997). Completeness and Decidability of Tense Logics Closely Related to Logics Above K. Journal of Symbolic Logic 62 (1):131-158.
    Tense logics formulated in the bimodal propositional language are investigated with respect to Kripke-completeness (completeness) and decidability. It is proved that all minimal tense extensions of modal logics of finite width (in the sense of K. Kine) as well as all minimal tense extensions of cofinal subframe logics (in the sense of M. Zakharyaschev) are complete. The decidability of all finitely axiomatizable minimal tense extensions of cofinal subframe logics is shown. A number of variations and extensions of these results are (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  25. Frank Wolter (1997). Superintuitionistic Companions of Classical Modal Logics. Studia Logica 58 (2):229-259.
    This paper investigates partitions of lattices of modal logics based on superintuitionistic logics which are defined by forming, for each superintuitionistic logic L and classical modal logic , the set L[] of L-companions of . Here L[] consists of those modal logics whose non-modal fragments coincide with L and which axiomatize if the law of excluded middle p V p is added. Questions addressed are, for instance, whether there exist logics with the disjunction property in L[], whether L[] contains a (...)
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  26. Frank Wolter (1997). The Structure of Lattices of Subframe Logics. Annals of Pure and Applied Logic 86 (1):47-100.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  27. Frank Wolter (1996). A Counterexample in Tense Logic. Notre Dame Journal of Formal Logic 37 (2):167-173.
    We construct a normal extension of K4 with the finite model property whose minimal tense extension is not complete with respect to Kripke semantics.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  28. Frank Wolter (1996). Properties of Tense Logics. Mathematical Logic Quarterly 42 (1):481-500.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  29. Frank Wolter (1996). Tense Logic Without Tense Operators. Mathematical Logic Quarterly 42 (1):145-171.
    No categories
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  30. Frank Wolter (1995). The Finite Model Property in Tense Logic. Journal of Symbolic Logic 60 (3):757-774.
    Tense logics in the bimodal propositional language are investigated with respect to the Finite Model Property. In order to prove positive results techniques from investigations of modal logics above K4 are extended to tense logic. General negative results show the limits of the transfer.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  31. Frank Wolter (1994). What is the Upper Part of the Lattice of Bimodal Logics? Studia Logica 53 (2):235 - 241.
    We define an embedding from the lattice of extensions ofT into the lattice of extensions of the bimodal logic with two monomodal operators 1 and 2, whose 2-fragment isS5 and 1-fragment is the logic of a two-element chain. This embedding reflects the fmp, decidability, completenes and compactness. It follows that the lattice of extension of a bimodal logic can be rather complicated even if the monomodal fragments of the logic belong to the upper part of the lattice of monomodal logics.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  32. Marcus Kracht & Frank Wolter (1991). Properties of Independently Axiomatizable Bimodal Logics. Journal of Symbolic Logic 56 (4):1469-1485.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation