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Natural Deduction for Hybrid Logic

Author:

Torben BraünerAuthors Info & Claims

Journal of Logic and Computation, Volume 14, Issue 3

Pages 329 - 353

https://doi.org/10.1093/logcom/14.3.329

Published: 01 June 2004 Publication History

Abstract

In this paper we give a natural deduction formulation of hybrid logic. Our natural deduction system can be extended with additional inference rules corresponding to conditions on the accessibility relations expressed by so-called geometric theories. Thus, we give natural deduction systems in a uniform way for a wide class of hybrid logics which appears to be impossible in the context of ordinary modal logic. We prove soundness and completeness and we prove a normalization theorem. We finally prove a result which says that normal derivations in the natural deduction system correspond to derivations in a cut-free Gentzen system.

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Braüner T(2019)Two Natural Deduction Systems for Hybrid LogicJournal of Logic, Language and Information10.1023/A:102618721532113:1(1-23)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1023/A%3A1026187215321
Park SIm H(2018)Type-safe higher-order channels with channel locality1Journal of Functional Programming10.1017/S095679680800698919:1(107-142)Online publication date: 24-Dec-2018
https://dl.acm.org/doi/10.1017/S0956796808006989
Rybakov V(2010)Modelling of Chance Discovery in variations of Linear Temporal Logic implementing agents' interactionInternational Journal of Advanced Intelligence Paradigms10.1504/IJAIP.2010.0305352:2/3(198-219)Online publication date: 1-Dec-2010
https://dl.acm.org/doi/10.1504/IJAIP.2010.030535
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Natural Deduction for Hybrid Logic

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Natural Deduction for First-Order Hybrid Logic

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cover image Journal of Logic and Computation

Journal of Logic and Computation Volume 14, Issue 3

June 2004

105 pages

ISSN:0955-792X

EISSN:1465-363X

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Oxford University Press, Inc.

United States

Publication History

Published: 01 June 2004

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Braüner T(2019)Two Natural Deduction Systems for Hybrid LogicJournal of Logic, Language and Information10.1023/A:102618721532113:1(1-23)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1023/A%3A1026187215321
Park SIm H(2018)Type-safe higher-order channels with channel locality1Journal of Functional Programming10.1017/S095679680800698919:1(107-142)Online publication date: 24-Dec-2018
https://dl.acm.org/doi/10.1017/S0956796808006989
Rybakov V(2010)Modelling of Chance Discovery in variations of Linear Temporal Logic implementing agents' interactionInternational Journal of Advanced Intelligence Paradigms10.1504/IJAIP.2010.0305352:2/3(198-219)Online publication date: 1-Dec-2010
https://dl.acm.org/doi/10.1504/IJAIP.2010.030535
Bolander THansen R(2010)Hybrid logical analyses of the ambient calculusInformation and Computation10.1016/j.ic.2009.01.006208:5(433-449)Online publication date: 1-May-2010
https://dl.acm.org/doi/10.1016/j.ic.2009.01.006
Park S(2006)A modal language for the safety of mobile valuesProceedings of the 4th Asian conference on Programming Languages and Systems10.1007/11924661_14(217-233)Online publication date: 8-Nov-2006
https://dl.acm.org/doi/10.1007/11924661_14
Braüner T(2005)Natural Deduction for First-Order Hybrid LogicJournal of Logic, Language and Information10.1007/s10849-005-3927-y14:2(173-198)Online publication date: 1-Mar-2005
https://dl.acm.org/doi/10.1007/s10849-005-3927-y

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Natural Deduction for Full S5 Modal Logic with Weak Normalization

Natural Deduction for First-Order Hybrid Logic

Axioms for classical, intuitionistic, and paraconsistent hybrid logic

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