Skip to main content
SpringerLink
Log in

Fuzzy Answer Set Programming: From Theory to Practice

  • Chapter
  • First Online:
Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications

Part of the book series: Studies in Computational Intelligence ((SCI,volume 835))

  • 316 Accesses

Abstract

In this chapter, we give an introduction to Fuzzy Answer Set Programming (FASP), as well as a description of a state-of-the-art FASP solver and its use in practice. FASP is an extension of Answer Set Programming (ASP), a well known declarative language that allows users to specify combinatorial search and optimization problems in an intuitive way. By combining ASP with fuzzy logic, FASP is capable of expressing continuous optimization problems. In the chapter, we provide a high-level explanation of how ASP is typically used for solving problems, and the role that an extension to FASP can play in applications. We present the syntax and semantics of FASP, and describe how FASP programs are used to encode problems. We subsequently explain how our solver finds the answer sets of a FASP program, and we illustrate the whole workflow using an application for modeling of gene regulatory networks.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Notes

  1. 1.

    The variable z is an auxiliary variable only intended to allow us to present a more concise expression here.

References

  1. Special issue on answer set programming, AI Magazine 37, 3 (2016)

    Google Scholar 

  2. M. Alviano, R. Peñaloza, Fuzzy answer sets approximations. Theory Pract. Log. Program. 13(4–5), 753–767 (2013)

    Article  MathSciNet  Google Scholar 

  3. M. Alviano, R. Peñaloza, Fuzzy answer set computation via satisfiability modulo theories. Theory Pract. Log. Program. 15, 588–603 (2015)

    Article  MathSciNet  Google Scholar 

  4. C. Baral, Knowledge Representation, Reasoning and Declarative Problem Solving (Cambridge University Press, 2003)

    Google Scholar 

  5. R. Ben-Eliyahu, R. Dechter, Propositional semantics for disjunctive logic programs. Ann. Math. Artif. Intell. 12(1–2), 53–87 (1994)

    Article  MathSciNet  Google Scholar 

  6. M. Blondeel, S. Schockaert, D. Vermeir, M. De Cock, Fuzzy answer set programming: an introduction, in Soft Computing: State of the Art Theory and Novel Applications, (Springer, Berlin, 2013), pp. 209–222

    Google Scholar 

  7. M. Blondeel, S. Schockaert, D. Vermeir, M. De Cock, Fuzzy Answer Set Programming: An Introduction, in Soft Computing: State of the Art Theory and Novel Applications, Studies in Fuzziness and Soft Computing, vol. 291, ed. by R.R. Yager, A.M. Abbasov, M.Z. Reformat, S.N. Shahbazova (Springer, Berlin Heidelberg, 2013), pp. 209–222

    Google Scholar 

  8. M. Blondeel, S. Schockaert, D. Vermeir, M. De Cock, Complexity of fuzzy answer set programming under Łukasiewicz semantics. Int. J. Approx. Reason. 55(9), 1971–2003 (2014)

    Article  Google Scholar 

  9. A. Bockmayr, H. Siebert, Programming Logics: Essays in Memory of Harald Ganzinger, Bio-Logics: Logical Analysis of Bioregulatory Networks (Springer, Berlin Heidelberg, 2013), pp. 19–34

    Google Scholar 

  10. C.V. Damásio, L.M. Pereira, Antitonic logic programs, in Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning, pp. 379–392 (2001)

    Google Scholar 

  11. J.P. Delgrande, T. Grote, A. Hunter, A general approach to the verification of cryptographic protocols using answer set programming, in Proceedings of the 10th International Conference in Logic Programming and Nonmonotonic Reasoning (LPNMR 2009), pp. 355–367 (2009)

    Google Scholar 

  12. J. Dix, G. Gottlob, W. Marek, Reducing disjunctive to non-disjunctive semantics by shift-operations. Fundam. Inform. 28(1), 87–100 (1996)

    Article  MathSciNet  Google Scholar 

  13. S. Dworschak, S. Grell, V.J. Nikiforova, T. Schaub, J. Selbig, Modeling biological networks by action languages via answer set programming. Constraints 13(1–2), 21–65 (2008)

    Article  MathSciNet  Google Scholar 

  14. E. Erdem, Theory and applications of answer set programming. Ph.D. thesis, (The University of Texas at Austin, 2002)

    Google Scholar 

  15. E. Erdem, V. Lifschitz, M. Wong, Wire routing and satisfiability planning. Comput. Log. CL 2000, 822–836 (2000)

    MathSciNet  MATH  Google Scholar 

  16. C. Espinosa-Soto, P. Padilla-Longoria, E.R. Alvarez-Buylla, A gene regulatory network model for cell-fate determination during arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles. Plant Cell Online 16(11), 2923–2939 (2004)

    Article  Google Scholar 

  17. A. Garg, A. Di Cara, I. Xenarios, L. Mendoza, G. De Micheli, Synchronous versus asynchronous modeling of gene regulatory networks. Bioinformatics 24(17), 1917–1925 (2008)

    Article  Google Scholar 

  18. M. Gebser, B. Kaufmann, R. Kaminski, M. Ostrowski, T. Schaub, M. Schneider, Potassco: the potsdam answer set solving collection. AI Commun. 24(2), 107–124 (2011)

    Article  MathSciNet  Google Scholar 

  19. M. Gebser, A. Konig, T. Schaub, S. Thiele, P. Veber, The BioASP library: ASP solutions for systems biology, in Proceedings of the 22nd IEEE International Conference on Tools with Artificial Intelligence (ICTAI), 2010, vol. 1, (IEEE, 2010), pp. 383–389

    Google Scholar 

  20. G. Grasso, N. Leone, M. Manna, F. Ricca, ASP at work: spin-off and applications of the DLV system. Log. Program., Knowl. Represent., Nonmonotonic Reason. 6565, 432–451 (2011)

    Article  Google Scholar 

  21. J. Guespin-Michel, M. Kaufman, Positive feedback circuits and adaptive regulations in bacteria. Acta Biotheor. 49(4), 207–218 (2001)

    Article  Google Scholar 

  22. I. Harvey, T. Bossomaier, Time out of joint: Attractors in asynchronous random boolean networks, in Proceedings of the Fourth European Conference on Artificial Life, pp. 67–75 (1997)

    Google Scholar 

  23. J. Janssen, S. Schockaert, D. Vermeir, M. De Cock, General fuzzy answer set programs, in: Fuzzy Logic and Applications (Springer, Berlin, 2009), pp. 352–359

    Google Scholar 

  24. S.A. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution (Oxford University Press, 1993)

    Google Scholar 

  25. N. Leone, G. Pfeifer, W. Faber, T. Eiter, G. Gottlob, S. Perri, F. Scarcello, The DLV system for knowledge representation and reasoning. ACM Trans. Comput. Log. 7(3), 499–562 (2006)

    Article  MathSciNet  Google Scholar 

  26. V. Lifschitz, What is answer set programming? in Proceedings of the 23rd AAAI Conference in Artificial Intelligence, vol. 8, (2008), pp. 1594–1597

    Google Scholar 

  27. M. Mushthofa, S. Schockaert, M. De Cock, A finite-valued solver for disjunctive fuzzy answer set programs. Proc. Eur. Conf. Artif. Intell. 2014, 645–650 (2014)

    MATH  Google Scholar 

  28. M. Mushthofa, S. Schockaert, M. De Cock, Solving disjunctive fuzzy answer set programs, in Proceedings of the 13th International Conference on Logic Programming and Non-monotonic Reasoning (2015), pp. 453–466

    Google Scholar 

  29. M. Mushthofa, G. Torres, Y. Van de Peer, K. Marchal, M. De Cock, ASP-G: an ASP-based method for finding attractors in genetic regulatory networks. Bioinformatics 30(21), 3086 (2014)

    Article  Google Scholar 

  30. R. Thomas, Boolean formalization of genetic control circuits. J. Theor. Biol. 42(3), 563–585 (1973)

    Article  Google Scholar 

  31. R. Thomas, Regulatory networks seen as asynchronous automata: a logical description. J. Theor. Biol. 153(1), 1–23 (1991)

    Article  MathSciNet  Google Scholar 

  32. D. Van Nieuwenborgh, M. De Cock, D. Vermeir, Fuzzy answer set programming, in Proceedings of the 10th European Conference on Logics in Artificial Intelligence (Springer, Berlin, 2006), pp. 359–372

    Google Scholar 

  33. M. Mushthofa, S. Schockaert, L.H. Hung, K. Marchal, M. De Cock, Modeling multi-valued biological interaction networks using fuzzy answer set programming. Fuzzy Sets and Systems, 345, 63–82 (2018)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium

    Mushthofa Mushthofa & Martine De Cock

  2. School of Computer Science & Informatics, Cardiff University, Cardiff, UK

    Steven Schockaert

  3. Department of Computer Science, IPB University, Bogor, Indonesia

    Mushthofa Mushthofa

  4. School of Engineering and Technology, University of Washington, Tacoma, USA

    Martine De Cock

Authors
  1. Mushthofa Mushthofa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steven Schockaert
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martine De Cock
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mushthofa Mushthofa .

Editor information

Editors and Affiliations

  1. Department of Teacher Education, University of Texas at El Paso, El Paso, TX, USA

    Olga Kosheleva

  2. Institute of Computational Technologies SB RAS, Novosibirsk, Russia

    Sergey P. Shary

  3. Johns Creek, GA, USA

    Gang Xiang

  4. Deptartment of Informatics, The State Russian Museum, Saint Petersburg, Russia

    Roman Zapatrin

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mushthofa, M., Schockaert, S., De Cock, M. (2020). Fuzzy Answer Set Programming: From Theory to Practice. In: Kosheleva, O., Shary, S., Xiang, G., Zapatrin, R. (eds) Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications. Studies in Computational Intelligence, vol 835. Springer, Cham. https://doi.org/10.1007/978-3-030-31041-7_12

Download citation

Publish with us

Policies and ethics

Search

Navigation