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  1. Rosalie Iemhoff, Logic for A.I. - Solutions.
    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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  2. Rosalie Iemhoff, Modal Logic.
    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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  3. Jeroen P. Goudsmit & Rosalie Iemhoff (2014). On Unification and Admissible Rules in Gabbay–de Jongh Logics. Annals of Pure and Applied Logic 165 (2):652-672.
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  4. Rosalie Iemhoff (2010). Kripke Models for Subtheories of CZF. 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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  5. Rosalie Iemhoff (2010). The Eskolemization of Universal Quantifiers. Annals of Pure and Applied Logic 162 (3):201-212.
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  6. Rosalie Iemhoff & George Metcalfe (2009). Proof Theory for Admissible Rules. Annals of Pure and Applied Logic 159 (1):171-186.
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  7. Matthias Baaz & Rosalie Iemhoff (2008). On Skolemization in Constructive Theories. 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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  8. Sergei Artemov & Rosalie Iemhoff (2007). The Basic Intuitionistic Logic of Proofs. 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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  9. Matthias Baaz & Rosalie Iemhoff (2006). Gentzen Calculi for the Existence Predicate. 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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  10. Matthias Baaz & Rosalie Iemhoff (2006). The Skolemization of Existential Quantifiers in Intuitionistic Logic. Annals of Pure and Applied Logic 142 (1):269-295.
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  11. Rosalie Iemhoff (2006). On the Rules of Intermediate Logics. 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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  12. Rosalie Iemhoff (2005). Intermediate Logics and Visser's Rules. 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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  13. Rosalie Iemhoff (2003). Preservativity Logic: An Analogue of Interpretability Logic for Constructive Theories. Mathematical Logic Quarterly 49 (3):230-249.
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  14. Rosalie Iemhoff (2002). Review: Albert Visser, Submodels of Kripke Models. [REVIEW] Bulletin of Symbolic Logic 8 (3):440-441.
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  15. Rosalie Iemhoff (2001). A(Nother) Characterization of Intuitionistic Propositional Logic. Annals of Pure and Applied Logic 113 (1-3):161-173.
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  16. Rosalie Iemhoff (2001). On the Admissible Rules of Intuitionistic Propositional Logic. 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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