36 found
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  1.  67
    On the admissible rules of intuitionistic propositional logic.Rosalie Iemhoff - 2001 - Journal of Symbolic Logic 66 (1):281-294.
    We present a basis for the admissible rules of intuitionistic propositional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility.
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  2.  51
    Consequence Relations and Admissible Rules.Rosalie Iemhoff - 2016 - Journal of Philosophical Logic 45 (3):327-348.
    This paper contains a detailed account of the notion of admissibility in the setting of consequence relations. It is proved that the two notions of admissibility used in the literature coincide, and it provides an extension to multi–conclusion consequence relations that is more general than the one usually encountered in the literature on admissibility. The notion of a rule scheme is introduced to capture rules with side conditions, and it is shown that what is generally understood under the extension of (...)
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  3.  61
    Questions and Dependency in Intuitionistic Logic.Ivano Ciardelli, Rosalie Iemhoff & Fan Yang - 2020 - Notre Dame Journal of Formal Logic 61 (1):75-115.
    In recent years, the logic of questions and dependencies has been investigated in the closely related frameworks of inquisitive logic and dependence logic. These investigations have assumed classical logic as the background logic of statements, and added formulas expressing questions and dependencies to this classical core. In this paper, we broaden the scope of these investigations by studying questions and dependency in the context of intuitionistic logic. We propose an intuitionistic team semantics, where teams are embedded within intuitionistic Kripke models. (...)
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  4.  66
    Proof theory for admissible rules.Rosalie Iemhoff & George Metcalfe - 2009 - Annals of Pure and Applied Logic 159 (1-2):171-186.
    Admissible rules of a logic are those rules under which the set of theorems of the logic is closed. In this paper, a Gentzen-style framework is introduced for analytic proof systems that derive admissible rules of non-classical logics. While Gentzen systems for derivability treat sequents as basic objects, for admissibility, the basic objects are sequent rules. Proof systems are defined here for admissible rules of classes of modal logics, including K4, S4, and GL, and also Intuitionistic Logic IPC. With minor (...)
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  5.  20
    Stable canonical rules.Guram Bezhanishvili, Nick Bezhanishvili & Rosalie Iemhoff - 2016 - Journal of Symbolic Logic 81 (1):284-315.
  6. Intermediate Logics and Visser's Rules.Rosalie Iemhoff - 2005 - Notre Dame Journal of Formal Logic 46 (1):65-81.
    Visser's rules form a basis for the admissible rules of . Here we show that this result can be generalized to arbitrary intermediate logics: Visser's rules form a basis for the admissible rules of any intermediate logic for which they are admissible. This implies that if Visser's rules are derivable for then has no nonderivable admissible rules. We also provide a necessary and sufficient condition for the admissibility of Visser's rules. We apply these results to some specific intermediate logics and (...)
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  7.  44
    On Rules.Rosalie Iemhoff - 2015 - Journal of Philosophical Logic 44 (6):697-711.
    This paper contains a brief overview of the area of admissible rules with an emphasis on results about intermediate and modal propositional logics. No proofs are given but many references to the literature are provided.
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  8.  35
    Logics of intuitionistic Kripke-Platek set theory.Rosalie Iemhoff & Robert Passmann - 2021 - Annals of Pure and Applied Logic 172 (10):103014.
    We investigate the logical structure of intuitionistic Kripke-Platek set theory , and show that the first-order logic of is intuitionistic first-order logic IQC.
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  9.  40
    A Syntactic Approach to Unification in Transitive Reflexive Modal Logics.Rosalie Iemhoff - 2016 - Notre Dame Journal of Formal Logic 57 (2):233-247.
    This paper contains a proof-theoretic account of unification in transitive reflexive modal logics, which means that the reasoning is syntactic and uses as little semantics as possible. New proofs of theorems on unification types are presented and these results are extended to negationless fragments. In particular, a syntactic proof of Ghilardi’s result that $\mathsf {S4}$ has finitary unification is provided. In this approach the relation between classical valuations, projective unifiers, and admissible rules is clarified.
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  10.  36
    Uniform interpolation and sequent calculi in modal logic.Rosalie Iemhoff - 2019 - Archive for Mathematical Logic 58 (1-2):155-181.
    A method is presented that connects the existence of uniform interpolants to the existence of certain sequent calculi. This method is applied to several modal logics and is shown to cover known results from the literature, such as the existence of uniform interpolants for the modal logic \. New is the result that \ has uniform interpolation. The results imply that for modal logics \ and \, which are known not to have uniform interpolation, certain sequent calculi cannot exist.
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  11.  54
    Structural completeness in propositional logics of dependence.Rosalie Iemhoff & Fan Yang - 2016 - Archive for Mathematical Logic 55 (7-8):955-975.
    In this paper we prove that three of the main propositional logics of dependence, none of which is structural, are structurally complete with respect to a class of substitutions under which the logics are closed. We obtain an analogous result with respect to stable substitutions, for the negative variants of some well-known intermediate logics, which are intermediate theories that are closely related to inquisitive logic.
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  12.  75
    On the rules of intermediate logics.Rosalie Iemhoff - 2006 - Archive for Mathematical Logic 45 (5):581-599.
    If the Visser rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How to characterize the admissible rules of intermediate logics for which not all of the Visser rules are admissible is not known. In this paper we give a brief overview of results on admissible rules in the context of intermediate logics. We apply these results to some well-known intermediate logics. We provide natural examples of logics for which the Visser (...)
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  13.  35
    A(nother) characterization of intuitionistic propositional logic.Rosalie Iemhoff - 2001 - Annals of Pure and Applied Logic 113 (1-3):161-173.
    In Iemhoff we gave a countable basis for the admissible rules of . Here, we show that there is no proper superintuitionistic logic with the disjunction property for which all rules in are admissible. This shows that, relative to the disjunction property, is maximal with respect to its set of admissible rules. This characterization of is optimal in the sense that no finite subset of suffices. In fact, it is shown that for any finite subset X of , for one (...)
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  14.  49
    On unification and admissible rules in Gabbay–de Jongh logics.Jeroen P. Goudsmit & Rosalie Iemhoff - 2014 - Annals of Pure and Applied Logic 165 (2):652-672.
    In this paper we study the admissible rules of intermediate logics. We establish some general results on extensions of models and sets of formulas. These general results are then employed to provide a basis for the admissible rules of the Gabbay–de Jongh logics and to show that these logics have finitary unification type.
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  15.  29
    Uniform interpolation and the existence of sequent calculi.Rosalie Iemhoff - 2019 - Annals of Pure and Applied Logic 170 (11):102711.
  16.  36
    Unification in intermediate logics.Rosalie Iemhoff & Paul Rozière - 2015 - Journal of Symbolic Logic 80 (3):713-729.
  17.  63
    Gentzen Calculi for the Existence Predicate.Matthias Baaz & Rosalie Iemhoff - 2006 - Studia Logica 82 (1):7-23.
    We introduce Gentzen calculi for intuitionistic logic extended with an existence predicate. Such a logic was first introduced by Dana Scott, who provided a proof system for it in Hilbert style. We prove that the Gentzen calculus has cut elimination in so far that all cuts can be restricted to very simple ones. Applications of this logic to Skolemization, truth value logics and linear frames are also discussed.
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  18.  42
    The Skolemization of existential quantifiers in intuitionistic logic.Matthias Baaz & Rosalie Iemhoff - 2006 - Annals of Pure and Applied Logic 142 (1):269-295.
    In this paper an alternative Skolemization method is introduced that, for a large class of formulas, is sound and complete with respect to intuitionistic logic. This class extends the class of formulas for which standard Skolemization is sound and complete and includes all formulas in which all strong quantifiers are existential. The method makes use of an existence predicate first introduced by Dana Scott.
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  19.  92
    The Basic Intuitionistic Logic of Proofs.Sergei Artemov & Rosalie Iemhoff - 2007 - Journal of Symbolic Logic 72 (2):439 - 451.
    The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F. In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found.
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  20.  48
    Preservativity logic: An analogue of interpretability logic for constructive theories.Rosalie Iemhoff - 2003 - Mathematical Logic Quarterly 49 (3):230-249.
    In this paper we study the modal behavior of Σ-preservativity, an extension of provability which is equivalent to interpretability for classical superarithmetical theories. We explain the connection between the principles of this logic and some well-known properties of HA, like the disjunction property and its admissible rules. We show that the intuitionistic modal logic given by the preservativity principles of HA known so far, is complete with respect to a certain class of frames.
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  21.  22
    Uniform Lyndon Interpolation for Basic Non-normal Modal Logics.Amirhossein Akbar Tabatabai, Rosalie Iemhoff & Raheleh Jalali - 2021 - In Alexandra Silva, Renata Wassermann & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation: 27th International Workshop, Wollic 2021, Virtual Event, October 5–8, 2021, Proceedings. Springer Verlag. pp. 287-301.
    In this paper, a proof-theoretic method to prove uniform Lyndon interpolation for non-normal modal logics is introduced and applied to show that the logics E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {E}$$\end{document}, M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {M}$$\end{document}, MC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {MC}$$\end{document}, EN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {EN}$$\end{document}, MN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {MN}$$\end{document} have that (...)
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  22.  30
    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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  23.  11
    Preservativity logic: An analogue of interpretability logic for constructive theories: An analogue of interpretability logic for constructive theories.Rosalie Iemhoff - 2003 - Mathematical Logic Quarterly 49 (3):230.
    In this paper we study the modal behavior of Σ‐preservativity, an extension of provability which is equivalent to interpretability for classical superarithmetical theories. We explain the connection between the principles of this logic and some well‐known properties of HA, like the disjunction property and its admissible rules. We show that the intuitionistic modal logic given by the preservativity principles of HA known so far, is complete with respect to a certain class of frames.
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  24.  45
    On Skolemization in constructive theories.Matthias Baaz & Rosalie Iemhoff - 2008 - Journal of Symbolic Logic 73 (3):969-998.
    In this paper a method for the replacement, in formulas, of strong quantifiers by functions is introduced that can be considered as an alternative to Skolemization in the setting of constructive theories. A constructive extension of intuitionistic predicate logic that captures the notions of preorder and existence is introduced and the method, orderization, is shown to be sound and complete with respect to this logic. This implies an analogue of Herbrand's theorem for intuitionistic logic. The orderization method is applied to (...)
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  25.  56
    Kripke models for subtheories of CZF.Rosalie Iemhoff - 2010 - Archive for Mathematical Logic 49 (2):147-167.
    In this paper a method to construct Kripke models for subtheories of constructive set theory is introduced that uses constructions from classical model theory such as constructible sets and generic extensions. Under the main construction all axioms except the collection axioms can be shown to hold in the constructed Kripke model. It is shown that by carefully choosing the classical models various instances of the collection axioms, such as exponentiation, can be forced to hold as well. The paper does not (...)
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  26.  34
    Skolemization in intermediate logics with the finite model property.Matthias Baaz & Rosalie Iemhoff - 2016 - Logic Journal of the IGPL 24 (3):224-237.
  27. (1 other version)A Modal Analysis of Some Principles of the Provability of Logic of Heyting Arithmetic.Rosalie Iemhoff - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 319-354.
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  28.  34
    Albert Visser. Submodels of Kripke models. Archive for mathematical logic, vol. 40 , pp. 277–295.Rosalie Iemhoff - 2002 - Bulletin of Symbolic Logic 8 (3):440-441.
  29.  74
    Logic for A.I. - Solutions.Rosalie Iemhoff - unknown
    Axiom 1 of K is the same as Axiom 1 in L, thus we have nothing to prove. Axiom 2 of K is 2(φ → ψ) → (2φ → 2ψ). We give a derivation of this formula in L: (φ → ψ) ∧ φ → ψ 2((φ → ψ) ∧ φ) → 2ψ (the rule from L) 2(φ → ψ) ∧ 2φ → 2ψ (axiom 3 of L and propositional logic) 2(φ → ψ) → (2φ → 2ψ) (propositional logic) Remain (...)
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  30. Logic, Language, Information, and Computation. WoLLIC 2019. Lecture Notes in Computer Science, Vol. 11541.Rosalie Iemhoff, Michael Moortgat & Ruy de Queiroz (eds.) - 2019 - Springer.
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  31. Logic, Language, Information, and Computation.Rosalie Iemhoff, Michael Moortgat & Ruy de Queiroz (eds.) - 2019 - Folli Publications on Logic, Language and Information.
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  32.  94
    Modal logic.Rosalie Iemhoff - unknown
    This text contains some basic facts about modal logic. For motivation, intuition and examples the reader should consult one of the standard textbooks in the field.
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  33.  26
    Special Issue on Admissible Rules and Unification.Rosalie Iemhoff & George Metcalfe - 2016 - Notre Dame Journal of Formal Logic 57 (4):441-442.
  34.  55
    The eskolemization of universal quantifiers.Rosalie Iemhoff - 2010 - Annals of Pure and Applied Logic 162 (3):201-212.
    This paper is a sequel to the papers Baaz and Iemhoff [4] and [6] in which an alternative skolemization method called eskolemization was introduced that, when restricted to strong existential quantifiers, is sound and complete for constructive theories. In this paper we extend the method to universal quantifiers and show that for theories satisfying the witness property it is sound and complete for all formulas. We obtain a Herbrand theorem from this, and apply the method to the intuitionistic theory of (...)
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  35.  21
    The G4i Analogue of a G3i Sequent Calculus.Rosalie Iemhoff - 2022 - Studia Logica 110 (6):1493-1506.
    This paper provides a method to obtain terminating analytic calculi for a large class of intuitionistic modal logics. For a given logic L with a cut-free calculus G that is an extension of G3ip the method produces a terminating analytic calculus that is an extension of G4ip and equivalent to G. G4ip was introduced by Roy Dyckhoff in 1992 as a terminating analogue of the calculus G3ip for intuitionistic propositional logic. Thus this paper can be viewed as an extension of (...)
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  36.  23
    Submodels of Kripke models. [REVIEW]Rosalie Iemhoff - 2002 - Bulletin of Symbolic Logic 8 (3):440-440.