Skip to main content
SpringerLink
Log in

Quasi-matrix Deontic Logic

  • Conference paper
Deontic Logic in Computer Science (DEON 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3065))

Included in the following conference series:

Abstract

We use non-Kripkean quasi-matrix semantics for the formalization of the systems S 3d , S 3dp and S 3dq of deontic logic. The system S 3d is weaker than the standard logic SDL . The semantics for S 3dp represents combination of quasi-matrix semantics and the semantics of truth value gluts, which allows S 3dp to avoid deontic explosion O A ∧ O¬A ⊃ O B. The system S 3dq rejects both deontic explosion and the formula O A ∧ O¬A ⊃ O A ∧ ¬O A, thus it allows to consider deontic dilemmas without classical contradictions.

The systems S 5d , S 5dp and S 5dq in which the two types of deontic operators are used, namely, strong and weak obligation (permission), can be built as an extension of the correspondent systems S 3d , S 3dp and S 3dq .

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

Access this chapter

Log in via an institution
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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alchourrón, C.E.: Philosophical foundations of deontic logic and the logic of defeasible conditionals. In: Meyer, J.-.J., Wieringa, R.J. (eds.) Deontic logic in computer science: normative system specification, pp. 43–84 (1993)

    Google Scholar 

  2. Bezhanishvili, M.N.: Hao Wang partial predicate calculi and their extensions allowing the iterations of implication. In: Logical Studies, Moscow (2001) (in Russian)

    Google Scholar 

  3. Chellas, B.: Modal logic: An introduction. Cambridge University Press, Cambridge (1980)

    MATH  Google Scholar 

  4. Cholvy, L., Cuppens, F.: Reasoning about norms provided by conflicting regulations. In: McNamara, P., Prakken, H. (eds.) Norms, logics and information systems: new studies in deontic logic and computer science, Amsterdam, pp. 247–262 (1999)

    Google Scholar 

  5. Ermolaeva, N.M.: O logikah, rodstvennyh ischisleniyu Hao Van’a. Nauchnotechnicheskaya informatsiya 2(8), 34–37 (1973) (in Russian)

    MathSciNet  Google Scholar 

  6. Goble, L.: Multiplex semantics for deontic logic. Nordic Journal of Philosophical Logic 5(2), 113–134 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Goble, L.: Deontic logic with relevance. In: McNamara, P., Prakken, H. (eds.) Norms, logics and information systems: new studies in deontic logic and computer science, Amsterdam, pp. 331–345 (1999)

    Google Scholar 

  8. Hansson, S.O.: Preference-based deontic logic (PDL). Journal of Philosophical Logic 19, 75–93 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hintikka, J.: Impossible possible worlds vindicated. Journal of Philosophical Logic 44, 475–484 (1975)

    Article  MathSciNet  Google Scholar 

  10. Horty, J.F.: Deontic logic as founded on nonmonotonic logic. Annals of Mathematics and Artificial Intelligence 9, 69–91

    Google Scholar 

  11. Ivlev, Y.V.: Modal logic. Moscow University Publ., Moscow (1991) (in Russian)

    MATH  Google Scholar 

  12. Kearns, J.: Modal semantics without possible worlds. Journal of Symbolic Logic 46(1), 77–86 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kouznetsov, A.M.: Quasi-matrix deontic logic, PhD-thesis, Moscow State University (1998) (in Russian)

    Google Scholar 

  14. Kouznetsov, A.M.: N-valued quasi-functional logic. In: Abstracts of the conference “Smirnov Readings”, Moscow, pp. 109–110 (2001) (in Russian)

    Google Scholar 

  15. Rose, A.: A formalization of the propositional calculus corresponding to Wang’s calculus of partial predicates. Zeitschrift fuer mathematische Logik und Grundlagen der Mathematik 9, 177–198 (1963)

    Article  MATH  Google Scholar 

  16. Schotch, P.K., Jennings, R.E.: Non-kripkean deontic logic. In: Hilpinen, R. (ed.) New studies in deontic logic, pp. 149–162 (1981)

    Google Scholar 

  17. van der Torre, L.W.N.: Reasoning about obligations: defeasibility in preferencebased deontic logic. Thesis Publishers, Amsterdam (1997)

    Google Scholar 

  18. Wang, H.: The calculus of partial predicates and its extension to set theory. Zeitschrift fuer mathematische Logik und Grundlagen der Mathematik 7, 283–288 (1961)

    Article  MATH  Google Scholar 

  19. von Wright, G.H.: Deontic logic. Mind 60 (1951)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, Kemerovo State University, Novokuznetsk Branch, 654041, Tsyolkovskogo St., 23, Novokuznetsk, Russia

    Andrei Kouznetsov

Authors
  1. Andrei Kouznetsov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computing, Imperial College, London, UK

    Alessio Lomuscio

  2. Department of Computer Science and Artificial Intelligence Center, The University of Georgia, 30602, Athens, GA,  

    Donald Nute

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kouznetsov, A. (2004). Quasi-matrix Deontic Logic. In: Lomuscio, A., Nute, D. (eds) Deontic Logic in Computer Science. DEON 2004. Lecture Notes in Computer Science(), vol 3065. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25927-5_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-25927-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22111-1

  • Online ISBN: 978-3-540-25927-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation