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  1. Torben Braüner (2014). Hybrid-Logical Reasoning in the Smarties and Sally-Anne Tasks. Journal of Logic, Language and Information 23 (4):415-439.
    The main aim of the present paper is to use a proof system for hybrid modal logic to formalize what are called false-belief tasks in cognitive psychology, thereby investigating the interplay between cognition and logical reasoning about belief. We consider two different versions of the Smarties task, involving respectively a shift of perspective to another person and to another time. Our formalizations disclose that despite this difference, the two versions of the Smarties task have exactly the same underlying logical structure. (...)
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  2. Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.) (2012). Advances in Modal Logic 9. College Publications.
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  3. Torben Braüner & Thomas Bolander (2009). Preface. Journal of Logic, Language and Information 18 (4):435-436.
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  4. Torben Braüner (2007). Why Does the Proof-Theory of Hybrid Logic Work so Well? Journal of Applied Non-Classical Logics 17 (4):521-543.
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  5. Torben Braüner (2006). Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic. Journal of Logic, Language and Information 15 (3):179-194.
    In this paper we give axiom systems for classical and intuitionistic hybrid logic. Our axiom systems can be extended with additional rules corresponding to conditions on the accessibility relation expressed by so-called geometric theories. In the classical case other axiomatisations than ours can be found in the literature but in the intuitionistic case no axiomatisations have been published. We consider plain intuitionistic hybrid logic as well as a hybridized version of the constructive and paraconsistent logic N4.
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  6. Torben Braüner (2006). Torben Braüner, Per Hasle and Peter Øhrstrøm/Preface Patrick Blackburn/Arthur Prior and Hybrid Logic B. Jack Copeland/Meredith, Prior, and the History of Possible Worlds Semantics. Synthese 150 (1):509-510.
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  7. Torben Braüner, Per Hasle & Peter Øhrstrøm (2006). Preface. Synthese 150 (3):327-328.
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  8. Torben BraÜner (2005). Natural Deduction for First-Order Hybrid Logic. Journal of Logic, Language and Information 14 (2):173-198.
    This is a companion paper to Braüner (2004b, Journal of Logic and Computation 14, 329–353) where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, (...)
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  9. Torben Braüner (2005). Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere. Studia Logica 81 (2):191 - 226.
    A hybrid logic is obtained by adding to an ordinary modal logic further expressive power in the form of a second sort of propositional symbols called nominals and by adding so-called satisfaction operators. In this paper we consider hybridized versions of S5 (“the logic of everywhere”) and the modal logic of inequality (“the logic of elsewhere”). We give natural deduction systems for the logics and we prove functional completeness results.
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  10. Torben Braüner (2004). Two Natural Deduction Systems for Hybrid Logic: A Comparison. [REVIEW] Journal of Logic, Language and Information 13 (1):1-23.
    In this paper two different natural deduction systems forhybrid logic are compared and contrasted.One of the systems was originally given by the author of the presentpaper whereasthe other system under consideration is a modifiedversion of a natural deductionsystem given by Jerry Seligman.We give translations in both directions between the systems,and moreover, we devise a set of reduction rules forthe latter system bytranslation of already known reduction rules for the former system.
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  11. Torben Braüner (2002). Modal Logic, Truth, and the Master Modality. Journal of Philosophical Logic 31 (4):359-386.
    In the paper (Braüner, 2001) we gave a minimal condition for the existence of a homophonic theory of truth for a modal or tense logic. In the present paper we generalise this result to arbitrary modal logics and we also show that a modal logic permits the existence of a homophonic theory of truth if and only if it permits the definition of a socalled master modality. Moreover, we explore a connection between the master modality and hybrid logic: We show (...)
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