First-Order Hybrid Logic

  • Torben Braüner
Part of the Applied Logic Series book series (APLS, volume 37)


In this chapter we introduce first-order hybrid logic and its proof-theory. The chapter is structured as follows. In the first section of the chapter we introduce first-order hybrid logic. In the second section we introduce a natural deduction system for first-order hybrid logic (taken from Braüner (2005b)) and in the third section we introduce an axiom system for first-order hybrid logic (also taken from Braüner (2005b)).


Axiom System Predicate Symbol Natural Deduction Hybrid Logic Predicate Abstraction 
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  1. C. Areces, P. Blackburn, and M. Marx. Repairing the interpolation theorem in quantified modal logic. Annals of Pure and Applied Logic, 124:287–299, 2003.CrossRefGoogle Scholar
  2. R.C. Barcan. A functional calculus of first order based on strict implication. Journal of Symbolic Logic, 11:1–16, 1946.CrossRefGoogle Scholar
  3. P. Blackburn and M. Marx. Tableaux for quantified hybrid logic. In U. Egly and C. Fermüller, editors, Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2002, volume 2381 of Lecture Notes in Artificial Intelligence, pages 38–52. Springer Berlin, 2002.CrossRefGoogle Scholar
  4. M. Fitting. First-order intensional logic. Annals of Pure and Applied Logic, 127:171–193, 2004. Essays in the memory of Alfred Tarski. Parts IV, V and VI.CrossRefGoogle Scholar
  5. A. Hazen. Expressive completeness in modal language. Journal of Philosophical Logic, 5:25–46, 1976.CrossRefGoogle Scholar
  6. H.T. Hodes. Some theorems on the expressive limitations of modal languages. Journal of Philosophical Logic, 13:13–26, 1984.CrossRefGoogle Scholar
  7. T. Jager. An actualist semantics for quantified modal logic. Notre Dame Journal of Formal Logic, 23:335–349, 1982.CrossRefGoogle Scholar
  8. D. Lewis. Counterpart theory and quantified modal logic. Journal of Philosophy, 65:113–126, 1968.CrossRefGoogle Scholar
  9. D. Lewis. Counterparts of persons and their bodies. Journal of Philosophy, 68:203–211, 1971.CrossRefGoogle Scholar
  10. H. Sturm and F. Wolter. First-order expressivity for S5-models: Modal vs. two-sorted languages. Journal of Philosophical Logic, 30:571–591, 2001.CrossRefGoogle Scholar
  11. M. Fitting and R.L. Mendelsohn. First-Order Modal Logic. Kluwer, 1998.Google Scholar
  12. J.W. Garson. Quantification in modal logic. In D.M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, 2nd Edition, volume 3, pages 267–323. Kluwer, 2001.Google Scholar
  13. G.E. Hughes and M.J. Cresswell. A New Introduction to Modal Logic. Routledge, 1996.Google Scholar
  14. M. Kracht and O. Kutz. The semantics of modal predicate logic I. Counterpart-frames. In F. Wolter, H. Wansing, M. de Rijke, and M. Zakharyaschev, editors, Advances in Modal Logic, Volume 3, pages 299–320. World Scientific, 2002.Google Scholar
  15. S. Lindstrøm and K. Segerberg. Modal logic and philosophy. In P. Blackburn, J. van Benthem, and F. Wolter, editors, Handbook of Modal Logic, pages 1149–1214. Elsevier, 2007.Google Scholar
  16. H.J. Ohlbach, A. Nonnengart, M. de Rijke, and D.M. Gabbay. Encoding two-valued non-classical logics in classical logic. In J.A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume 1, pages 1403–1486. MIT Press, 2001.Google Scholar
  17. A. Plantinga. Actualism and possible worlds. In M. Davidson, editor, Essays in the Metaphysics of Modality, pages 103–121. Oxford University Press, 2003. Originally published in Theoria, 42:139–160, 1976.Google Scholar
  18. W.V.O. Quine. Three grades of modal involvement. In The Ways of Paradox and Other Essays, pages 156–174. Random House, 1953.Google Scholar
  19. J. van Benthem. Modal Logic and Classical Logic. Bibliopolis, 1983.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Programming, Logic and Intelligent Systems Research Group (PLIS)Roskilde UniversityRoskildeDenmark

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