Skip to main content

First-Order Hybrid Logic

  • Chapter
  • First Online:
Hybrid Logic and its Proof-Theory

Part of the book series: Applied Logic Series ((APLS,volume 37))

Abstract

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)).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • 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.

    Article  Google Scholar 

  • R.C. Barcan. A functional calculus of first order based on strict implication. Journal of Symbolic Logic, 11:1–16, 1946.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  Google Scholar 

  • A. Hazen. Expressive completeness in modal language. Journal of Philosophical Logic, 5:25–46, 1976.

    Article  Google Scholar 

  • H.T. Hodes. Some theorems on the expressive limitations of modal languages. Journal of Philosophical Logic, 13:13–26, 1984.

    Article  Google Scholar 

  • T. Jager. An actualist semantics for quantified modal logic. Notre Dame Journal of Formal Logic, 23:335–349, 1982.

    Article  Google Scholar 

  • D. Lewis. Counterpart theory and quantified modal logic. Journal of Philosophy, 65:113–126, 1968.

    Article  Google Scholar 

  • D. Lewis. Counterparts of persons and their bodies. Journal of Philosophy, 68:203–211, 1971.

    Article  Google Scholar 

  • H. Sturm and F. Wolter. First-order expressivity for S5-models: Modal vs. two-sorted languages. Journal of Philosophical Logic, 30:571–591, 2001.

    Article  Google Scholar 

  • M. Fitting and R.L. Mendelsohn. First-Order Modal Logic. Kluwer, 1998.

    Google Scholar 

  • 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 

  • G.E. Hughes and M.J. Cresswell. A New Introduction to Modal Logic. Routledge, 1996.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • J. van Benthem. Modal Logic and Classical Logic. Bibliopolis, 1983.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Torben Braüner .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Braüner, T. (2011). First-Order Hybrid Logic. In: Hybrid Logic and its Proof-Theory. Applied Logic Series, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0002-4_6

Download citation

Publish with us

Policies and ethics