49 found
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  1.  14
    Tools and Techniques in Modal Logic.Marcus Kracht - 1999 - 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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  2.  9
    Modal Logic.Marcus Kracht - 2002 - Bulletin of Symbolic Logic 8 (2):299-301.
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  3.  41
    Properties of Independently Axiomatizable Bimodal Logics.Marcus Kracht & Frank Wolter - 1991 - Journal of Symbolic Logic 56 (4):1469-1485.
  4.  38
    On Extensions of Intermediate Logics by Strong Negation.Marcus Kracht - 1998 - 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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  5.  41
    Normal Monomodal Logics Can Simulate All Others.Marcus Kracht & Frank Wolter - 1999 - 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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  6.  34
    Interpreted Languages and Compositionality.Marcus Kracht - 2011 - 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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  7. Simulation and Transfer Results in Modal Logic – a Survey.Marcus Kracht & Frank Wolter - 1997 - 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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  8.  34
    An Almost General Splitting Theorem for Modal Logic.Marcus Kracht - 1990 - 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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  9. Splittings and the Finite Model Property.Marcus Kracht - 1993 - 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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  10.  14
    Power and Weakness of the Modal Display Calculus.Marcus Kracht - 1996 - In H. Wansing (ed.), Proof Theory of Modal Logic. Kluwer Academic Publishers. pp. 93--121.
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  11.  31
    Semisimple Varieties of Modal Algebras.Tomasz Kowalski & Marcus Kracht - 2006 - 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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  12.  70
    On the Semantics of Locatives.Marcus Kracht - 2002 - 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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  13. The Emergence of Syntactic Structure.Marcus Kracht - 2007 - 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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  14.  4
    Normal Monomodal Logics Can Simulate All Others.Marcus Kracht & Frank Wolter - 1999 - 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 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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  15.  23
    Prefinitely Axiomatizable Modal and Intermediate Logics.Marcus Kracht - 1993 - Mathematical Logic Quarterly 39 (1):301-322.
    A logic Λ bounds a property P if all proper extensions of Λ have P while Λ itself does not. We construct logics bounding finite axiomatizability and logics bounding finite model property in the lattice of intermediate logics and in the lattice of normal extensions of K4.3. MSC: 03B45, 03B55.
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  16.  21
    Are Logical Languages Compositional?Marcus Kracht - 2013 - 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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  17.  36
    Even More About the Lattice of Tense Logics.Marcus Kracht - 1992 - 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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  18.  11
    Syntactic Codes and Grammar Refinement.Marcus Kracht - 1995 - Journal of Logic, Language and Information 4 (1):41-60.
  19.  49
    Judgment and Consequence Relations.Marcus Kracht - 2010 - Journal of Applied Non-Classical Logics 20 (4):423-435.
    In this paper I argue that a variety of consequence relations can be subsumed under a common core. The reduction proceeds by taking the unconditional consequence, or judgment, as basic and deriving the conditional consequence via a uniform abstraction scheme. A specific outcome is that it is better not to base such a scheme on the semantic notion of a matrix and valuation but rather on theories and substitutions. I will also briefly look at consequence relations that are not reducible (...)
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  20.  6
    Book Review: V. V. Rybakov. Admissibility of Logical Inference Rules. [REVIEW]Marcus Kracht - 1999 - Notre Dame Journal of Formal Logic 40 (4):578-587.
  21.  15
    Gnosis.Marcus Kracht - 2011 - 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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  22.  75
    Is There a Genuine Modal Perspective on Feature Structures?Marcus Kracht - 1995 - Linguistics and Philosophy 18 (4):401 - 458.
  23.  59
    Lattices of Modal Logics and Their Groups of Automorphisms.Marcus Kracht - 1999 - Annals of Pure and Applied Logic 100 (1-3):99-139.
    The present paper investigates the groups of automorphisms for some lattices of modal logics. The main results are the following. The lattice of normal extensions of S4.3, NExtS4.3, has exactly two automorphisms, NExtK.alt1 has continuously many automorphisms. Moreover, any automorphism of NExtS4 fixes all logics of finite codimension. We also obtain the following characterization of pretabular logics containing S4: a logic properly extends a pretabular logic of NExtS4 iff its lattice of extensions is finite and linear.
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  24.  27
    Technical Modal Logic.Marcus Kracht - 2011 - Philosophy Compass 6 (5):350-359.
  25. REVIEWS-Fibring Logics.D. Gabbay & Marcus Kracht - 2004 - Bulletin of Symbolic Logic 10 (2):209-210.
     
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  26.  24
    Modal Logics That Need Very Large Frames.Marcus Kracht - 1999 - 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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  27.  20
    Atomic Incompleteness or How to Kill One Bird with Two Stones.Marcus Kracht & Tomasz Kowalski - 2001 - Bulletin of the Section of Logic 30 (2):71-78.
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  28. REVIEWS-Modal Logic.P. Blackburn, M. De Rijke, Y. Venema & Marcus Kracht - 2002 - Bulletin of Symbolic Logic 8 (2):299-300.
  29. Advances in Modal Logic, Vol. 1.Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev - 2000 - Studia Logica 65 (3):440-442.
  30. Advances in Modal Logic.Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.) - 1998 - CSLI Publications.
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  31.  15
    Aspects of Space.Marcus Kracht - 2015 - The Baltic International Yearbook of Cognition, Logic and Communication 10 (1).
    It is argued that spatial expressions come together with an encoding of the space called "aspect", which changes as we climb up the syntactic tree. The changing nature of aspect is necessary in order to simplify the meanings of elements. What appears to be a rather peculiar property of an element will be perfectly natural once we acknowledge that the elements compute on the space viewed in a particular way. Coordinates are always rooted in the landmark, for example. Thus, for (...)
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  32.  20
    A Solution to a Problem of Urquhart.Marcus Kracht - 1991 - Journal of Philosophical Logic 20 (3):285 - 286.
  33.  9
    Book Review. [REVIEW]Marcus Kracht - 1997 - Journal of Logic, Language and Information 6 (3):344-350.
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  34.  4
    Features in Phonological Theory.Marcus Kracht - 2003 - In Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences Ii. Kluwer Academic Publishers. pp. 123--149.
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  35.  6
    Fibring Logics.Marcus Kracht - 2004 - Bulletin of Symbolic Logic 10 (2):209-211.
  36.  10
    Invariant Logics.Marcus Kracht - 2002 - Mathematical Logic Quarterly 48 (1):29-50.
    A moda logic Λ is called invariant if for all automorphisms α of NExt K, α = Λ. An invariant ogic is therefore unique y determined by its surrounding in the attice. It wi be established among other that a extensions of K.alt1S4.3 and G.3 are invariant ogics. Apart from the results that are being obtained, this work contributes to the understanding of the combinatorics of finite frames in genera, something wich has not been done except for transitive frames. Certain (...)
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  37. Logic and Syntax.Marcus Kracht - 2000 - In Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 2. CSLI Publications. pp. 355-384.
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  38. Logic and Syntax.Marcus Kracht - 2000 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 355-384.
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  39.  5
    Logics of Infinite Depth.Marcus Kracht - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 435-448.
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  40.  8
    Modal Logic. [REVIEW]Marcus Kracht - 2002 - Bulletin of Symbolic Logic 8 (2):299-300.
  41.  19
    Michiel van Lambalgen and Fritz Hamm. The Proper Treatment of Events. Explorations in Semantics, No. 4. Blackwell Publishing, Oxford, 2005, Xii + 251 Pp. [REVIEW]Marcus Kracht - 2006 - Bulletin of Symbolic Logic 12 (1):139-141.
  42.  2
    Notes on the Space Requirements for Checking Satisgiability in Modal Logics.Marcus Kracht - 2003 - In Philippe Balbiani, Nobu-Yuki Suzuki, Frank Wolter & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 4. CSLI Publications. pp. 243-264.
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  43.  1
    Notes on the Space Requirements for Checking Satisgiability in Modal Logics.Marcus Kracht - 2003 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 243-264.
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  44.  35
    Patrick Blackburn, Maarten De Rijke, and Yde Venema. Modal Logic. Cambridge Tracts in Theoretical Computer Science, No. 53. Cambridge University Press, Cambridge, New York, Etc., 2001, Xxii + 554 Pp. [REVIEW]Marcus Kracht - 2002 - Bulletin of Symbolic Logic 8 (2):299-301.
  45.  38
    Syntax in Chains.Marcus Kracht - 2001 - 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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  46.  58
    The Grammar of Code Switching.Marcus Kracht & Udo Klein - 2014 - Journal of Logic, Language and Information 23 (3):313-329.
    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 . In this paper we provide a formal analysis of code switching.
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  47. The Semantics of Modal Predicate Logic I. Counterpart-Frames.Marcus Kracht & Oliver Kutz - 2002 - In Frank Wolter, Heinrich Wansing, Maarten de Rijke & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 3. CSLI Publications. pp. 299-320.
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  48. The Semantics of Modal Predicate Logic I. Counterpart-Frames.Marcus Kracht & Oliver Kutz - 2002 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 299-320.
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  49.  28
    Review: Patrick Blackburn, Maarten de Rijke, Yde Venema, Modal Logic. [REVIEW]Marcus Kracht - 2002 - Bulletin of Symbolic Logic 8 (2):299-301.