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  1.  61
    Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
    This is a companion paper to Braüner 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, we give an axiom system first-order hybrid logic.
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  2.  37
    Two Natural Deduction Systems for Hybrid Logic: A Comparison. [REVIEW]Torben Braüner - 2004 - 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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  3.  15
    Intuitionistic Hybrid Logic.Torben Braüner & Valeria de Paiva - 2006 - Journal of Applied Logic 4 (3):231-255.
    Hybrid logics are a principled generalization of both modal logics and description logics, a standard formalism for knowledge representation. In this paper we give the first constructive version of hybrid logic, thereby showing that it is possible to hybridize constructive modal logics. Alternative systems are discussed, but we fix on a reasonable and well-motivated version of intuitionistic hybrid logic and prove essential proof-theoretical results for a natural deduction formulation of it. Our natural deduction system is also extended with additional inference (...)
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  4. Modal Logic, Truth, and the Master Modality.Torben Braüner - 2002 - 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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  5.  38
    Hybrid-Logical Reasoning in the Smarties and Sally-Anne Tasks.Torben Braüner - 2014 - 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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  6.  5
    Being Deceived: Information Asymmetry in Second‐Order False Belief Tasks.Torben Braüner, Patrick Blackburn & Irina Polyanskaya - forthcoming - Topics in Cognitive Science.
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  7.  25
    Willem Conradie and Valentin Goranko, Logic and Discrete Mathematics: A Concise Introduction. Wiley, 2015, Pp. 450. ISBN-13: 978-1-118-75127-5 $42, ISBN-10: 978-1-118-75127-2 $37.99. [REVIEW]Torben Braüner - 2018 - Studia Logica 106 (3):671-673.
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  8.  30
    Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere.Torben Braüner - 2005 - 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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  9.  54
    Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic.Torben Braüner - 2006 - 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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  10. 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.Torben Braüner - 2006 - Synthese 150 (1):509-510.
     
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  11.  6
    Synthetic Completeness Proofs for Seligman-Style Tableau Systems.Klaus Frovin Jørgensen, Patrick Blackburn, Thomas Bolander & Torben Braüner - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 302-321.
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  12.  6
    Many-Valued Hybrid Logic.Jens Ulrik Hansen, Thomas Bolander & Torben Braüner - 2008 - In Carlos Areces & Robert Goldblatt (eds.), Advances in Modal Logic, Volume 7. CSLI Publications. pp. 111-132.
    In this paper we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be "intermediate" logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained (...)
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  13.  14
    Why Does the Proof-Theory of Hybrid Logic Work so Well?Torben Braüner - 2007 - Journal of Applied Non-Classical Logics 17 (4):521-543.
    This is primarily a conceptual paper. The goal of the paper is to put into perspective the proof-theory of hybrid logic and in particular, try to give an answer to the following question: Why does the proof-theory of hybrid logic work so well compared to the proof-theory of ordinary modal logic? Roughly, there are two different kinds of proof systems for modal logic: Systems where the formulas involved in the rules are formulas of the object language, that is, ordinary modal-logical (...)
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  14.  3
    Functional Completenes for a Natural Deduction Formulation of Hybridized S5.Torben Braüner - 2003 - In Philippe Balbiani, Nobu-Yuki Suzuki, Frank Wolter & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 4. CSLI Publications. pp. 31-49.
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  15.  3
    Preface.Torben Braüner & Thomas Bolander - 2009 - Journal of Logic, Language and Information 18 (4):435-436.
  16. Advances in Modal Logic 9.Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.) - 2012 - College Publications.
     
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  17. Homophonic Theory of Truth for Tense Logic.Torben Braüner - 2002 - In Frank Wolter, Heinrich Wansing, Maarten de Rijke & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 3. CSLI Publications. pp. 59-72.
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  18. Proceedings of the International Workshop on Hybrid Logic 2007 (HyLo 2007).Jørgen Villadsen, Thomas Bolander & Torben Braüner (eds.) - 2007
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