Skip to main content

Unification in Modal Logic

  • Conference paper
  • First Online:
Book cover Logic and Its Applications (ICLA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11600))

Included in the following conference series:

Abstract

Let \(\varphi _{1},\ldots ,\varphi _{n}\) and \(\psi \) be some formulas.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  1. Baader, F.: On the complexity of Boolean unification. Inf. Process. Lett. 67, 215–220 (1998)

    Article  MathSciNet  Google Scholar 

  2. Baader, F., Borgwardt, S., Morawska, B.: Extending unification in \(\cal{EL}\) towards general TBoxes. In: Brewka, G. et al. (eds.) Principles of Knowledge Representation and Reasoning, pp. 568–572. AAAI Press (2012)

    Google Scholar 

  3. Baader, F., Ghilardi, S.: Unification in modal and description logics. Log. J. IGPL 19, 705–730 (2011)

    Article  MathSciNet  Google Scholar 

  4. Baader, F., Morawska, B.: Unification in the description logic \(\cal{EL}\). In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 350–364. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02348-4_25

    Chapter  Google Scholar 

  5. Baader, F., Narendran, P.: Unification of concept terms in description logics. J. Symb. Comput. 31, 277–305 (2001)

    Article  MathSciNet  Google Scholar 

  6. Babenyshev, S., Rybakov, V.: Unification in linear temporal logic \(LTL\). Ann. Pure Appl. Log. 162, 991–1000 (2011)

    Article  MathSciNet  Google Scholar 

  7. Babenyshev, S., Rybakov, V., Schmidt, R., Tishkovsky, D.: A tableau method for checking rule admissibility in \(S4\). Electron. Notes Theor. Comput. Sci. 262, 17–32 (2010)

    Article  MathSciNet  Google Scholar 

  8. Balbiani, P.: Remarks about the unification type of some non-symmetric non-transitive modal logics. Log. J. IGPL (2018, to appear)

    Google Scholar 

  9. Balbiani, P., Gencer, Ç.: \(KD\) is nullary. J. Appl. Non Class. Log. 27, 196–205 (2017)

    Article  MathSciNet  Google Scholar 

  10. Balbiani, P., Gencer, Ç.: Unification in epistemic logics. J. Appl. Non Class. Log. 27, 91–105 (2017)

    Article  MathSciNet  Google Scholar 

  11. Balbiani, P., Tinchev, T.: Unification in modal logic \(Alt_{1}\). In: Advances in Modal Logic, pp. 117–134. College Publications (2016)

    Google Scholar 

  12. Balbiani, P., Tinchev, T.: Elementary unification in modal logic \(KD45\). J. Appl. Log. IFCoLog J. Log. Appl. 5, 301–317 (2018)

    MATH  Google Scholar 

  13. Chagrov, A.: Decidable modal logic with undecidable admissibility problem. Algebra i Logika 31, 83–93 (1992)

    Article  Google Scholar 

  14. Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford University Press, Oxford (1997)

    MATH  Google Scholar 

  15. Cintula, P., Metcalfe, G.: Admissible rules in the implication-negation fragment of intuitionistic logic. Ann. Pure Appl. Log. 162, 162–171 (2010)

    Article  MathSciNet  Google Scholar 

  16. Dzik, W.: Unitary unification of \(S5\) modal logics and its extensions. Bull. Sect. Log. 32, 19–26 (2003)

    MathSciNet  MATH  Google Scholar 

  17. Dzik, W.: Unification Types in Logic. Wydawnicto Uniwersytetu Slaskiego, Katowice (2007)

    MATH  Google Scholar 

  18. Dzik, W.: Remarks on projective unifiers. Bull. Sect. Log. 40, 37–46 (2011)

    MathSciNet  MATH  Google Scholar 

  19. Dzik, W., Wojtylak, P.: Projective unification in modal logic. Log. J. IGPL 20, 121–153 (2012)

    Article  MathSciNet  Google Scholar 

  20. Fernández Gil, O.: Hybrid Unification in the Description Logic \(\cal{EL}\). Master thesis of Technische Universität Dresden (2012)

    Google Scholar 

  21. Gencer, Ç.: Description of modal logics inheriting admissible rules for \(K4\). Log. J. IGPL 10, 401–411 (2002)

    Article  MathSciNet  Google Scholar 

  22. Gencer, Ç., de Jongh, D.: Unifiability in extensions of \(K4\). Log. J. IGPL 17, 159–172 (2009)

    Article  MathSciNet  Google Scholar 

  23. Ghilardi, S.: Unification in intuitionistic logic. J. Symb. Log. 64, 859–880 (1999)

    Article  MathSciNet  Google Scholar 

  24. Ghilardi, S.: Best solving modal equations. Ann. Pure Appl. Log. 102, 183–198 (2000)

    Article  MathSciNet  Google Scholar 

  25. Ghilardi, S.: A resolution/tableaux algorithm for projective approximations in \(IPC\). Log. J. IGPL 10, 229–243 (2002)

    Article  MathSciNet  Google Scholar 

  26. Ghilardi, S., Sacchetti, L.: Filtering unification and most general unifiers in modal logic. J. Symb. Log. 69, 879–906 (2004)

    Article  MathSciNet  Google Scholar 

  27. Iemhoff, R.: On the admissible rules of intuitionistic propositional logic. J. Symb. Comput. 66, 281–294 (2001)

    MathSciNet  MATH  Google Scholar 

  28. Iemhoff, R., Metcalfe, G.: Proof theory for admissible rules. Ann. Pure Appl. Log. 159, 171–186 (2009)

    Article  MathSciNet  Google Scholar 

  29. Jer̆ábek, E.: Complexity of admissible rules. Arch. Math. Log. 46, 73–92 (2007)

    Article  MathSciNet  Google Scholar 

  30. Jer̆ábek, E.: Blending margins: the modal logic \(K\) has nullary unification type. J. Log. Comput. 25, 1231–1240 (2015)

    Article  MathSciNet  Google Scholar 

  31. Martin, U., Nipkow, T.: Boolean unification – the story so far. J. Symb. Comput. 7, 275–293 (1989)

    Article  MathSciNet  Google Scholar 

  32. Rozière, P.: Règles admissibles en calcul propositionnel intuitionniste. Thesis of the University Paris VII (1993)

    Google Scholar 

  33. Rybakov, V.: A criterion for admissibility of rules in the model system \(S4\) and the intuitionistic logic. Algebra Log. 23, 369–384 (1984)

    Article  Google Scholar 

  34. Rybakov, V.: Bases of admissible rules of the logics \(S4\) and \(Int\). Algebra Log. 24, 55–68 (1985)

    Article  Google Scholar 

  35. Rybakov, V.: Admissibility of Logical Inference Rules. Elsevier, Amsterdam (1997)

    MATH  Google Scholar 

  36. Rybakov, V.: Construction of an explicit basis for rules admissible in modal system \(S4\). Math. Log. Q. 47, 441–446 (2001)

    Article  MathSciNet  Google Scholar 

  37. Rybakov, V., Gencer, Ç., Oner, T.: Description of modal logics inheriting admissible rules for \(S4\). Log. J. IGPL 7, 655–664 (1999)

    Article  MathSciNet  Google Scholar 

  38. Rybakov, V., Terziler, M., Gencer, Ç.: An essay on unification and inference rules for modal logics. Bull. Sect. Log. 28, 145–157 (1999)

    MathSciNet  MATH  Google Scholar 

  39. Rybakov, V., Terziler, M., Gencer, Ç.: Unification and passive inference rules for modal logics. J. Appl. Non Class. Log. 10, 369–377 (2000)

    Article  MathSciNet  Google Scholar 

  40. Rybakov, V., Terziler, M., Gencer, Ç.: On self-admissible quasi-characterizing inference rules. Stud. Logica. 65, 417–428 (2000)

    Article  MathSciNet  Google Scholar 

  41. Wolter, F., Zakharyaschev, M.: Undecidability of the unification and admissibility problems for modal and description logics. ACM Trans. Comput. Log. 9, 25:1–25:20 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Philippe Balbiani .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer-Verlag GmbH Germany, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Balbiani, P. (2019). Unification in Modal Logic. In: Khan, M., Manuel, A. (eds) Logic and Its Applications. ICLA 2019. Lecture Notes in Computer Science(), vol 11600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58771-3_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-58771-3_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-58770-6

  • Online ISBN: 978-3-662-58771-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics