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  1. Marcus Kracht & Udo Klein (forthcoming). The Grammar of Code Switching. Journal of Logic, Language and Information:1-17.
    The idea that language is a homogeneous code is a massive simplification. In actual fact, we constantly use a wide array of codes, be they other languages, dialects, registers, or special purpose codes (for bank account numbers, book numbers, shoe sizes, and so on). In this paper we provide a formal analysis of code switching.
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  2. Marcus Kracht (2013). Are Logical Languages Compositional? Studia Logica 101 (6):1319-1340.
    In this paper I argue that in contrast to natural languages, logical languages typically are not compositional. This does not mean that the meaning of expressions cannot be determined at all using some well-defined set of rules. It only means that the meaning of an expression cannot be determined without looking at its form. If one is serious about the compositionality of a logic, the only possibility I see is to define it via abstraction from a variable free language.
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  3. Marcus Kracht (2011). Gnosis. Journal of Philosophical Logic 40 (3):397 - 420.
    The transition from form to meaning is not neatly layered: there is no point where form ends and content sets in. Rather, there is an almost continuous process that converts form into meaning. That process cannot always take a straight line. Very often we hit barriers in our mind, due to the inability to understand the exact content of the sentence just heard. The standard division between formula and interpretation (or value) should therefore be given up when talking about the (...)
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  4. Marcus Kracht (2011). Interpreted Languages and Compositionality. Springer.
    This book argues that languages are composed of sets of ‘signs’, rather than ‘strings’. This notion, first posited by de Saussure in the early 20th century, has for decades been neglected by linguists, particularly following Chomsky’s heavy critiques of the 1950s. Yet since the emergence of formal semantics in the 1970s, the issue of compositionality has gained traction in the theoretical debate, becoming a selling point for linguistic theories. Yet the concept of ‘compositionality’ itself remains ill-defined, an issue this book (...)
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  5. Marcus Kracht (2011). Technical Modal Logic. Philosophy Compass 6 (5):350-359.
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  6. Marcus Kracht (2010). Judgment and Consequence Relations. Journal of Applied Non-Classical Logics 20 (4):423-435.
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  7. Marcus Kracht (2007). The Emergence of Syntactic Structure. Linguistics and Philosophy 30 (1):47 - 95.
    The present paper is the result of a long struggle to understand how the notion of compositionality can be used to motivate the structure of a sentence. While everyone seems to have intuitions about which proposals are compositional and which ones are not, these intuitions generally have no formal basis. What is needed to make such arguments work is a proper understanding of what meanings are and how they can be manipulated. In particular, we need a definition of meaning that (...)
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  8. Tomasz Kowalski & Marcus Kracht (2006). Semisimple Varieties of Modal Algebras. Studia Logica 83 (1-3):351 - 363.
    In this paper we show that a variety of modal algebras of finite type is semisimple iff it is discriminator iff it is both weakly transitive and cyclic. This fact has been claimed already in [4] (based on joint work by the two authors) but the proof was fatally flawed.
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  9. Marcus Kracht (2006). Van Lambalgen Michiel and Hamm Fritz. The Proper Treatment of Events. Explorations in Semantics, No. 4. Blackwell Publishing, Oxford, 2005, Xii+ 251 Pp. [REVIEW] Bulletin of Symbolic Logic 12 (1):139-141.
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  10. M. Van Lambalgen, F. Hamm & Marcus Kracht (2006). REVIEWS-The Proper Treatment of Events. Bulletin of Symbolic Logic 12 (1):139-140.
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  11. D. Gabbay & Marcus Kracht (2004). REVIEWS-Fibring Logics. Bulletin of Symbolic Logic 10 (2):209-210.
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  12. Marcus Kracht (2004). Fibring Logics. Bulletin of Symbolic Logic 10 (2):209-211.
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  13. Marcus Kracht (2003). Features in Phonological Theory. In. In Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences Ii. Kluwer. 123--149.
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  14. P. Blackburn, M. De Rijke, Y. Venema & Marcus Kracht (2002). REVIEWS-Modal Logic. Bulletin of Symbolic Logic 8 (2):299-300.
     
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  15. Marcus Kracht (2002). Blackburn Patrick, De Rijke Maarten, and Venema Yde. Modal Logic. Cambridge Tracts in Theoretical Computer Science, No. 53. Cambridge University Press, Cambridge, New York, Etc., 2001, Xxii+ 554 Pp. [REVIEW] Bulletin of Symbolic Logic 8 (2):299-301.
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  16. Marcus Kracht (2002). Invariant Logics. Mathematical Logic Quarterly 48 (1):29-50.
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  17. Marcus Kracht (2002). On the Semantics of Locatives. Linguistics and Philosophy 25 (2):157-232.
    The present paper deals with the semantics of locative expressions. Our approach is essentially model-theoretic, using basic geometrical properties of the space-time continuum. We shall demonstrate that locatives consist of two layers: the first layer defines a location and the second a type of movement with respect to that location. The elements defining these layers, called localisersand modalisers, tend to form a unit, which is typically either an adposition or a case marker. It will be seen that this layering is (...)
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  18. Marcus Kracht (2002). Referent Systems and Relational Grammar. Journal of Logic, Language and Information 11 (2):251-286.
    Relational Grammar (RG) was introduced in the 1970s as a theory of grammatical relations and relation change, for example, passivization, dative shift, and raising. Furthermore, the idea behind RG was that transformations as originally designed in generative grammar were unable to capture the common kernel of, e.g., passivization across languages. The researchconducted within RG has uncovered a wealth of phenomena for which it could produce a satisfactory analysis. Although the theory of Government and Binding has answered some of the complaints, (...)
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  19. Marcus Kracht (2002). Review: Patrick Blackburn, Maarten de Rijke, Yde Venema, Modal Logic. [REVIEW] Bulletin of Symbolic Logic 8 (2):299-301.
  20. Marcus Kracht (2001). Syntax in Chains. Linguistics and Philosophy 24 (4):467-530.
    In transformational grammar the notion of a chain has been central ever since its introduction in the early 80's. However, an insightful theory of chains has hitherto been missing. This paper develops such a theory of chains. Though it is applicable to virtually all chains, we shall focus on movement-induced chains. It will become apparent that chains are far from innocuous. A proper formulation of the structures and algorithms involved is quite a demanding task. Furthermore, we shall show that it (...)
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  21. Marcus Kracht & Tomasz Kowalski (2001). Atomic Incompleteness or How to Kill One Bird with Two Stones. Bulletin of the Section of Logic 30 (2):71-78.
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  22. Marcus Kracht (1999). Lattices of Modal Logics and Their Groups of Automorphisms. Annals of Pure and Applied Logic 100 (1-3):99-139.
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  23. Marcus Kracht (1999). Tools and Techniques in Modal Logic. Elsevier.
    This book treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory and transfer theory and is intended as a course in modal logic for students who have had prior contact with modal logic and who wish to study it more deeply. It presupposes training in mathematical or logic. Very little specific knowledge is presupposed, most results which are needed are proved in this book.
     
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  24. Marcus Kracht (1999). Book Review: V. V. Rybakov. Admissibility of Logical Inference Rules. [REVIEW] Notre Dame Journal of Formal Logic 40 (4):578-587.
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  25. Marcus Kracht (1999). Modal Logics That Need Very Large Frames. Notre Dame Journal of Formal Logic 40 (2):141-173.
    The Kuznetsov-Index of a modal logic is the least cardinal such that any consistent formula has a Kripke-model of size if it has a Kripke-model at all. The Kuznetsov-Spectrum is the set of all Kuznetsov-Indices of modal logics with countably many operators. It has been shown by Thomason that there are tense logics with Kuznetsov-Index . Futhermore, Chagrov has constructed an extension of K4 with Kuznetsov-Index . We will show here that for each countable ordinal there are logics with Kuznetsov-Index (...)
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  26. 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.
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  27. Marcus Kracht (1998). On Extensions of Intermediate Logics by Strong Negation. Journal of Philosophical Logic 27 (1):49-73.
    In this paper we will study the properties of the least extension n(Λ) of a given intermediate logic Λ by a strong negation. It is shown that the mapping from Λ to n(Λ) is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n(Λ). This summarizes results that can be found already in [13, 14] and [4]. Furthermore, we determine the (...)
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  28. Marcus Kracht (1997). Book Review. [REVIEW] Journal of Logic, Language and Information 6 (3).
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  29. 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 (...)
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  30. Marcus Kracht (1996). Power and Weakness of the Modal Display Calculus. In H. Wansing (ed.), Proof Theory of Modal Logic. Kluwer. 93--121.
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  31. Marcus Kracht (1995). Is There a Genuine Modal Perspective on Feature Structures? Linguistics and Philosophy 18 (4):401 - 458.
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  32. Marcus Kracht (1993). Prefinitely Axiomatizable Modal and Intermediate Logics. Mathematical Logic Quarterly 39 (1):301-322.
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  33. Marcus Kracht (1993). Splittings and the Finite Model Property. Journal of Symbolic Logic 58 (1):139-157.
    An old conjecture of modal logics states that every splitting of the major systems K4, S4, G and Grz has the finite model property. In this paper we will prove that all iterated splittings of G have fmp, whereas in the other cases we will give explicit counterexamples. We also introduce a proof technique which will give a positive answer for large classes of splitting frames. The proof works by establishing a rather strong property of these splitting frames namely that (...)
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  34. Marcus Kracht (1992). Even More About the Lattice of Tense Logics. Archive for Mathematical Logic 31 (4):243-257.
    The present paper is based on [11], where a number of conjectures are made concerning the structure of the lattice of normal extensions of the tense logicKt. That paper was mainly dealing with splittings of and some sublattices, and this is what I will concentrate on here as well. The main tool in analysing the splittings of will be the splitting theorem of [8]. In [11] it was conjectured that each finite subdirectly irreducible algebra splits the lattice of normal extensions (...)
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  35. Marcus Kracht (1991). A Solution to a Problem of Urquhart. Journal of Philosophical Logic 20 (3):285 - 286.
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  36. Marcus Kracht & Frank Wolter (1991). Properties of Independently Axiomatizable Bimodal Logics. Journal of Symbolic Logic 56 (4):1469-1485.
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  37. Marcus Kracht (1990). An Almost General Splitting Theorem for Modal Logic. Studia Logica 49 (4):455 - 470.
    Given a normal (multi-)modal logic a characterization is given of the finitely presentable algebras A whose logics L A split the lattice of normal extensions of . This is a substantial generalization of Rautenberg [10] and [11] in which is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by Blok [2] that for all cycle-free and finite A L A splits the lattice of normal extensions of K. Although we (...)
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