Skip to main content
SpringerLink
Log in

Knowledge of Uncertain Worlds: Programming with Logical Constraints

  • Conference paper
  • First Online:
Logical Foundations of Computer Science (LFCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11972))

Included in the following conference series:

Abstract

Programming with logic for sophisticated applications must deal with recursion and negation, which have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a unified language, DA logic, for design and analysis logic, based on the unifying founded semantics and constraint semantics, that support the power and ease of programming with different intended semantics. The key idea is to provide meta-constraints, support the use of uncertain information in the form of either undefined values or possible combinations of values, and promote the use of knowledge units that can be instantiated by any new predicates, including predicates with additional arguments.

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 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. Apt, K.R., Blair, H.A., Walker, A.: Towards a theory of declarative knowledge. In: Foundations of Deductive Databases and Logic Programming, pp. 89–148. Morgan Kaufman (1988)

    Google Scholar 

  2. Apt, K.R., Bol, R.N.: Logic programming and negation: a survey. J. Log. Program. 19, 9–71 (1994)

    Article  MathSciNet  Google Scholar 

  3. Bruynooghe, M., Denecker, M., Truszczynski, M.: First order logic with inductive definitions for model-based problem solving. AI Mag. 37(3), 69–80 (2016)

    Article  Google Scholar 

  4. Chan, D.: Constructive negation based on the completed database. In: Proceedings of the 5th International Conference and Symposium on Logic Programming, pp. 111–125. MIT Press (1988)

    Google Scholar 

  5. Clark, K.L.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Databases, pp. 293–322. Plenum Press (1978)

    Google Scholar 

  6. Dasseville, I., Van der Hallen, M., Janssens, G., Denecker, M.: Semantics of templates in a compositional framework for building logics. Theory Pract. Log. Program. 15(4–5), 681–695 (2015)

    Article  MathSciNet  Google Scholar 

  7. Denecker, M., Ternovska, E.: A logic of nonmonotone inductive definitions. ACM Trans. Comput. Log. 9(2), 14 (2008)

    Article  MathSciNet  Google Scholar 

  8. Dung, P.M.: On the relations between stable and well-founded semantics of logic programs. Theoret. Comput. Sci. 105(1), 7–25 (1992)

    Article  MathSciNet  Google Scholar 

  9. Ershov, Y.L., Goncharov, S.S., Sviridenko, D.I.: Semantic foundations of programming. In: Budach, L., Bukharajev, R.G., Lupanov, O.B. (eds.) FCT 1987. LNCS, vol. 278, pp. 116–122. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-18740-5_28

    Chapter  Google Scholar 

  10. Fitting, M.: A Kripke-Kleene semantics for logic programs. J. Log. Program. 2(4), 295–312 (1985)

    Article  MathSciNet  Google Scholar 

  11. Fitting, M.: Fixpoint semantics for logic programming: a survey. Theoret. Comput. Sci. 278(1), 25–51 (2002)

    Article  MathSciNet  Google Scholar 

  12. Foo, N.Y., Rao, A.S., Taylor, A., Walker, A.: Deduced relevant types and constructive negation. In: Proceedings of the 5th International Conference and Symposium on Logic Programming, pp. 126–139 (1988)

    Google Scholar 

  13. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proceedings of the 5th International Conference and Symposium on Logic Programming, pp. 1070–1080. MIT Press (1988)

    Google Scholar 

  14. Hou, P., De Cat, B., Denecker, M.: FO(FD): extending classical logic with rule-based fixpoint definitions. Theory Pract. Log. Program. 10(4–6), 581–596 (2010)

    Article  MathSciNet  Google Scholar 

  15. Jaffar, J., Lassez, J.-L., Maher, M.J.: Some issues and trends in the semantics of logic programming. In: Shapiro, E. (ed.) ICLP 1986. LNCS, vol. 225, pp. 223–241. Springer, Heidelberg (1986). https://doi.org/10.1007/3-540-16492-8_78

    Chapter  MATH  Google Scholar 

  16. Lin, F., Zhao, Y.: ASSAT: computing answer sets of a logic program by sat solvers. Artif. Intell. 157(1–2), 115–137 (2004)

    Article  MathSciNet  Google Scholar 

  17. Liu, Y.A., Stoller, S.D.: Founded semantics and constraint semantics of logic rules. Computing Research Repository arXiv:1606.06269 [cs.LO], June 2016 (Revised April 2017)

  18. Liu, Y.A., Stoller, S.D.: Founded semantics and constraint semantics of logic rules. In: Artemov, S., Nerode, A. (eds.) LFCS 2018. LNCS, vol. 10703, pp. 221–241. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-72056-2_14

    Chapter  Google Scholar 

  19. Lloyd, J.W., Topor, R.W.: Making Prolog more expressive. J. Log. Program. 1(3), 225–240 (1984)

    Article  MathSciNet  Google Scholar 

  20. Przymusinski, T.C.: Well-founded and stationary models of logic programs. Ann. Math. Artif. Intell. 12(3), 141–187 (1994)

    Article  MathSciNet  Google Scholar 

  21. Ramakrishnan, R., Ullman, J.D.: A survey of deductive database systems. J. Log. Program. 23(2), 125–149 (1995)

    Article  MathSciNet  Google Scholar 

  22. Sato, T., Tamaki, H.: Transformational logic program synthesis. In: Proceedings of the International Conference on Fifth Generation Computer Systems, pp. 195–201 (1984)

    Google Scholar 

  23. Stuckey, P.J.: Constructive negation for constraint logic programming. In: Proceedings of the 6th Annual IEEE Symposium on Logic in Computer Science, pp. 328–339 (1991)

    Google Scholar 

  24. Truszczynski, M.: An introduction to the stable and well-founded semantics of logic programs. In: Kifer, M., Liu, Y.A. (eds.) Declarative Logic Programming: Theory, Systems, and Applications, pp. 121–177. ACM and Morgan & Claypool (2018)

    Google Scholar 

  25. Van Gelder, A., Ross, K., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported in part by NSF under grants CCF-1414078, CNS-1421893, and IIS-1447549.

Author information

Authors and Affiliations

  1. Computer Science Department, Stony Brook University, Stony Brook, NY, USA

    Yanhong A. Liu & Scott D. Stoller

Authors
  1. Yanhong A. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Scott D. Stoller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanhong A. Liu .

Editor information

Editors and Affiliations

  1. The Graduate Center, CUNY, New York, NY, USA

    Sergei Artemov

  2. Cornell University, Ithaca, NY, USA

    Anil Nerode

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Liu, Y.A., Stoller, S.D. (2020). Knowledge of Uncertain Worlds: Programming with Logical Constraints. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2020. Lecture Notes in Computer Science(), vol 11972. Springer, Cham. https://doi.org/10.1007/978-3-030-36755-8_8

Download citation

Publish with us

Policies and ethics

Search

Navigation