Journal of Applied Logic 4 (3):231-255 (2006)

Valeria Correa Vaz De Paiva
University of Birmingham
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 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 constructive hybrid logics. This shows that constructive hybrid logics are a viable enterprise and opens up the way for future applications.
Keywords Hybrid logic  Modal logic  Intuitionistic logic
Categories (categorize this paper)
DOI 10.1016/j.jal.2005.06.009
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 56,903
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Basic Proof Theory.Roy Dyckhoff - 2001 - Bulletin of Symbolic Logic 7 (2):280-280.
Topology Via Logic.P. T. Johnstone & Steven Vickers - 1991 - Journal of Symbolic Logic 56 (3):1101.

Add more references

Citations of this work BETA

Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic.Torben Braüner - 2006 - Journal of Logic, Language and Information 15 (3):179-194.
A Family of Gödel Hybrid Logics.Didier Galmiche & Yakoub Salhi - 2010 - Journal of Applied Logic 8 (4):371-385.

View all 6 citations / Add more citations

Similar books and articles

Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic.Torben Braüner - 2006 - Journal of Logic, Language and Information 15 (3):179-194.
Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
Hybrid Identities and Hybrid Equational Logic.Klaus Denecke - 1995 - Mathematical Logic Quarterly 41 (2):190-196.
Bi-Simulating in Bi-Intuitionistic Logic.Guillermo Badia - 2016 - Studia Logica 104 (5):1037-1050.
Modal Logic, Truth, and the Master Modality.Torben Braüner - 2002 - Journal of Philosophical Logic 31 (4):359-386.
Truth-Maker Semantics for Intuitionistic Logic.Kit Fine - 2014 - Journal of Philosophical Logic 43 (2-3):549-577.
Reverse Mathematics and Completeness Theorems for Intuitionistic Logic.Takeshi Yamazaki - 2001 - Notre Dame Journal of Formal Logic 42 (3):143-148.
Towards Intuitionistic Dynamic Logic.J. W. Degen & J. M. Werner - 2006 - Logic and Logical Philosophy 15 (4):305-324.
A Note on Dual-Intuitionistic Logic.Norihiro Kamide - 2003 - Mathematical Logic Quarterly 49 (5):519.


Added to PP index

Total views
20 ( #513,468 of 2,409,595 )

Recent downloads (6 months)
3 ( #245,496 of 2,409,595 )

How can I increase my downloads?


My notes