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Dick de Jongh [29]Dick H. J. de Jongh [2]
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  1.  14
    Stable Formulas in Intuitionistic Logic.Nick Bezhanishvili & Dick de Jongh - 2018 - Notre Dame Journal of Formal Logic 59 (3):307-324.
    In 1995 Visser, van Benthem, de Jongh, and Renardel de Lavalette introduced NNIL-formulas, showing that these are exactly the formulas preserved under taking submodels of Kripke models. In this article we show that NNIL-formulas are up to frame equivalence the formulas preserved under taking subframes of frames, that NNIL-formulas are subframe formulas, and that subframe logics can be axiomatized by NNIL-formulas. We also define a new syntactic class of ONNILLI-formulas. We show that these are the formulas preserved in monotonic images (...)
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  2. Provability Logics for Relative Interpretability.Frank Veltman & Dick De Jongh - 1990 - In Petio Petrov Petkov (ed.), Mathematical Logic. Proceedings of the Heyting '88 Summer School. New York, NY, USA: pp. 31-42.
    In this paper the system IL for relative interpretability is studied.
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  3. Modal Completeness of ILW.Dick De Jongh & Frank Veltman - 1999 - In Jelle Gerbrandy, Maarten Marx, Maarten de Rijke & Yde Venema (eds.), Essays Dedicated to Johan van Benthem on the Occasion of His 50th Birthday. Amsterdam University Press.
    This paper contains a completeness proof for the system ILW, a rather bewildering axiom system belonging to the family of interpretability logics. We have treasured this little proof for a considerable time, keeping it just for ourselves. Johan’s ftieth birthday appears to be the right occasion to get it out of our wine cellar.
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  4.  16
    The Decidability of Dependency in Intuitionistic Propositional Logi.Dick de Jongh & L. A. Chagrova - 1995 - Journal of Symbolic Logic 60 (2):498-504.
    A definition is given for formulae $A_1,\ldots,A_n$ in some theory $T$ which is formalized in a propositional calculus $S$ to be (in)dependent with respect to $S$. It is shown that, for intuitionistic propositional logic $\mathbf{IPC}$, dependency (with respect to $\mathbf{IPC}$ itself) is decidable. This is an almost immediate consequence of Pitts' uniform interpolation theorem for $\mathbf{IPC}$. A reasonably simple infinite sequence of $\mathbf{IPC}$-formulae $F_n(p, q)$ is given such that $\mathbf{IPC}$-formulae $A$ and $B$ are dependent if and only if at least (...)
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  5.  38
    Intermediate Logics and the de Jongh Property.Dick de Jongh, Rineke Verbrugge & Albert Visser - 2011 - Archive for Mathematical Logic 50 (1-2):197-213.
    We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.
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  6.  18
    Generic Generalized Rosser Fixed Points.Dick H. J. de Jongh & Franco Montagna - 1987 - Studia Logica 46 (2):193-203.
    To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical completeness theorem with respect to PA is obtained for LR.
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  7.  14
    On the Proof of Solovay's Theorem.Dick de Jongh, Marc Jumelet & Franco Montagna - 1991 - Studia Logica 50 (1):51-69.
    Solovay's 1976 completeness result for modal provability logic employs the recursion theorem in its proof. It is shown that the uses of the recursion theorem can in this proof replaced by the diagonalization lemma for arithmetic and that, in effect, the proof neatly fits the framework of another, enriched, system of modal logic so that any arithmetical system for which this logic is sound is strong enough to carry out the proof, in particular $\text{I}\Delta _{0}+\text{EXP}$ . The method is adapted (...)
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  8.  5
    Explicit Fixed Points in Interpretability Logic.Dick de Jongh & Albert Visser - 1991 - Studia Logica 50 (1):39-49.
    The problem of Uniqueness and Explicit Definability of Fixed Points for Interpretability Logic is considered. It turns out that Uniqueness is an immediate corollary of a theorem of Smoryński.
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  9.  22
    Provable Fixed Points.Dick De Jongh & Franco Montagna - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (3):229-250.
  10. Intensional Logics.Dick De Jongh & Frank Veltman - unknown
    This first chapter contains an introduction to modal logic. In section 1.1 the syntactic side of the matter is discussed, and in section 1.2 the subject is approached from a semantic point of view.
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  11.  19
    Extendible Formulas in Two Variables in Intuitionistic Logic.Nick Bezhanishvili & Dick de Jongh - 2012 - Studia Logica 100 (1-2):61-89.
    We give alternative characterizations of exact, extendible and projective formulas in intuitionistic propositional calculus IPC in terms of n-universal models. From these characterizations we derive a new syntactic description of all extendible formulas of IPC in two variables. For the formulas in two variables we also give an alternative proof of Ghilardi’s theorem that every extendible formula is projective.
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  12.  20
    Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers.J. A. G. Groenendijk, Dick de Jongh & M. J. B. Stokhof (eds.) - 1986 - Foris Publications.
    Semantic Automata Johan van Ben them. INTRODUCTION An attractive, but never very central idea in modern semantics has been to regard linguistic expressions ...
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  13.  14
    Provable Fixed Points.Dick De Jongh & Franco Montagna - 1988 - Mathematical Logic Quarterly 34 (3):229-250.
  14.  7
    Rosser Orderings and Free Variables.Dick de Jongh & Franco Montagna - 1991 - Studia Logica 50 (1):71-80.
    It is shown that for arithmetical interpretations that may include free variables it is not the Guaspari-Solovay system R that is arithmetically complete, but their system R⁻. This result is then applied to obtain the nonvalidity of some rules under arithmetical interpretations including free variables, and to show that some principles concerning Rosser orderings with free variables cannot be decided, even if one restricts onself to "usual" proof predicates.
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  15.  19
    Much Shorter Proofs.Dick de Jongh & Franco Montagna - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (3):247-260.
  16.  3
    Much Shorter Proofs.Dick de Jongh & Franco Montagna - 1989 - Mathematical Logic Quarterly 35 (3):247-260.
  17. Interpolation, Definability and Fixed Points in Interpretability Logics.Carlos Areces, Eva Hoogland & Dick de Jongh - 2000 - In Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 2. CSLI Publications. pp. 53-76.
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  18.  7
    Interpretability in PRA.Marta Bílková, Dick de Jongh & Joost J. Joosten - 2009 - Annals of Pure and Applied Logic 161 (2):128-138.
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  19.  9
    Properties of Intuitionistic Provability and Preservativity Logics.Rosalie Iemhoff, Dick de Jongh & Chunlai Zhou - 2005 - Logic Journal of the IGPL 13 (6):615-636.
    We study the modal properties of intuitionistic modal logics that belong to the provability logic or the preservativity logic of Heyting Arithmetic. We describe the □-fragment of some preservativity logics and we present fixed point theorems for the logics iL and iPL, and show that they imply the Beth property. These results imply that the fixed point theorem and the Beth property hold for both the provability and preservativity logic of Heyting Arithmetic. We present a frame correspondence result for the (...)
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  20.  9
    The Kuznetsov-Gerčiu and Rieger-Nishimura Logics.Guram Bezhanishvili, Nick Bezhanishvili & Dick de Jongh - 2008 - Logic and Logical Philosophy 17 (1-2):73-110.
    We give a systematic method of constructing extensions of the Kuznetsov-Gerčiu logic KG without the finite model property (fmp for short), and show that there are continuum many such. We also introduce a new technique of gluing of cyclic intuitionistic descriptive frames and give a new simple proof of Gerčiu’s result [9, 8] that all extensions of the Rieger-Nishimura logic RN have the fmp. Moreover, we show that each extension of RN has the poly-size model property, thus improving on [9]. (...)
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  21.  6
    Provable Fixed Points.Much Shorter Proofs.Rosser Orderings in Bimodal Logics.Much Shorter Proofs: A Bimodal Investigation. [REVIEW]Lev D. Beklemishev, Dick de Jongh, Franco Montagna & Alessandra Carbone - 1993 - Journal of Symbolic Logic 58 (2):715.
  22.  6
    Interpretability In.Marta Bílková, Dick de Jongh & Joost J. Joosten - 2009 - Annals of Pure and Applied Logic 161 (2):128-138.
    In this paper, we study IL(), the interpretability logic of . As is neither an essentially reflexive theory nor finitely axiomatizable, the two known arithmetical completeness results do not apply to : IL() is not or . IL() does, of course, contain all the principles known to be part of IL, the interpretability logic of the principles common to all reasonable arithmetical theories. In this paper, we take two arithmetical properties of and see what their consequences in the modal logic (...)
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  23.  4
    Preface.Dick de Jongh & Albert Visser - 1993 - Annals of Pure and Applied Logic 61 (1-2):1.
  24. Interpolation, Definability and Fixed Points in Interpretability Logics.Carlos Areces, Eva Hoogland & Dick de Jongh - 2000 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 53-76.
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  25. Foundations of Pragmatics and Lexical Semantics.J. A. G. Groenendijk, Dick de Jongh & M. J. B. Stokhof (eds.) - 1986 - Providence, Ri, Usa, Foris Publications ;.
     
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