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Abductive Question-Answer System (\(\mathsf {AQAS}\)) for Classical Propositional Logic

  • Szymon Chlebowski
  • Andrzej Gajda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10333)

Abstract

We propose a new approach to modelling abductive reasoning by means of an abductive question-answer system. We introduce the concept of an abductive question which is the starting point of abductive reasoning. The result of applying the question processing procedure is a question, which is simpler than the initial one. \(\mathsf {AQAS}\) generates abductive hypotheses that fulfil certain criteria in one step, i.e. processes of generation and evaluation of abductive hypotheses are integrated.

Keywords

Logic of questions Inferential Erotetic Logic Erotetic calculi Abduction 

Notes

Acknowledgements

This work has been supported by the Polish National Science Center, grant no. 2012/04/A/HS1/00715 (first author) and DEC-2013/10/E/HS1/00172 (second author).

References

  1. 1.
    Aliseda, A.: Abductive Reasoning. Logical Investigations into Discovery and Explanation. Springer, Dordrecht (2006). doi: 10.1007/1-4020-3907-7 zbMATHGoogle Scholar
  2. 2.
    Chlebowski, S., Leszczyńska-Jasion, D.: Dual erotetic calculi and the minimal LFI. Studia Logica 103(6), 1245–1278 (2015). doi: 10.1007/s11225-015-9617-0 MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ciardelli, I., Roelofsen, F.: Inquisitive logic. J. Philos. Log. 40, 55–94 (2011). doi: 10.1007/s10992-010-9142-6 MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ciardelli, I., Groenendijk, J., Roelofsen, F.: On the semantics and logic of declaratives and interrogatives. Synthese (2013). doi: 10.1007/s11229-s013-0352-7
  5. 5.
    Denecker, M., Kakas, A.: Abduction in logic programming. In: Kakas, A.C., Sadri, F. (eds.) Computational Logic: Logic Programming and Beyond. LNCS, vol. 2407, pp. 402–436. Springer, Heidelberg (2002). doi: 10.1007/3-540-45628-7_16 CrossRefGoogle Scholar
  6. 6.
    Fitting, M.: First-Order Logic and Automated Theorem Proving. Springer, New York (1996). doi: 10.1007/978-1-4612-2360-3 CrossRefzbMATHGoogle Scholar
  7. 7.
    Hintikka, J.: What is abduction? The fundamental problem of contemporary epistemology. In: Inquiry as Inquiry: A Logic of Scientific Discovery, pp. 91–113. Springer, Dordrecht (1999). doi: 10.1007/978-94-015-9313-7_4
  8. 8.
    Hintikka, J.: Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning. Cambridge University Press, Cambridge (2007). ISBN: 9780521616515CrossRefGoogle Scholar
  9. 9.
    Kakas, A.C., Kowalski, R.A., Toni, F.: Abductive logic programming. J. Log. Comput. 2(6), 719–770 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Komosiński, M., Kupś, A., Leszczyńska-Jasion, D., Urbański, M.: Identifying efficient abductive hypotheses using multi-criteria dominance relation. ACM Trans. Comput. Log. (TOCL) 15(4), 28:1–28:20 (2014). doi: 10.1145/2629669 zbMATHGoogle Scholar
  11. 11.
    Leszczyńska-Jasion, D.: Socratic proofs for some normal modal propositional logics. Logique et Analyse 47(185–188), 259–285 (2004)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Magnani, L.: Abductive Cognition. The Epistemological and Eco-cognitive Dimensions of Hypothetical Reasoning. Springer, Dordrecht (2009). doi: 10.1007/s10838-011-9146-0 zbMATHGoogle Scholar
  13. 13.
    Mayer, M.C., Pirri, F.: Propositional abduction in modal logic. Log. J. IGPL 3(6), 907–919 (1995). doi: 10.1093/jigpal/3.6.907 MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Meheus, J., Batens, D.: A formal logic of abductive reasoning. Log. J. IGPL 14(2), 221–236 (2006). doi: 10.1093/jigpal/jzk015 MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Peirce, C.S.: Collected Works. Harvard University Press, Cambridge (1931). Republished in 1958Google Scholar
  16. 16.
    Sintonen, M.: Reasoning to hypotheses: where do questions come? Found. Sci. 9(3), 249–266 (2004). doi: 10.1023/B:FODA.0000042842.55251.c1 CrossRefGoogle Scholar
  17. 17.
    Smullyan, R.M.: First-Order Logic. Springer, Heidelberg (1968)CrossRefzbMATHGoogle Scholar
  18. 18.
    Thagard, P.: Abductive inference: from philosophical analysis to neural mechanisms. In: Feeney, A., Heit, E. (eds.) Inductive Reasoning: Cognitive, Mathematical, and Neuroscientific Approaches, pp. 226–247. Cambridge University Press, Cambridge (2007). doi: 10.1017/CBO9780511619304.010 CrossRefGoogle Scholar
  19. 19.
    Urbański, M.: Rozumowania abdukcyjne. Wydawnictwo Naukowe UAM, Poznań (2009)Google Scholar
  20. 20.
    Urbański, M., Wiśniewski, A.: On search for law-like statements as abductive hypotheses by socratic transformations. In: Baskent, C. (ed.) Perspectives on Interrogative Models of Inquiry. Developments in Inquiry and Questions, vol. 8, pp. 111–127. Springer, Cham (2016). doi: 10.1007/978-3-319-20762-9_7 CrossRefGoogle Scholar
  21. 21.
    Wiśniewski, A.: Socratic proofs. J. Philos. Log. 33(3), 299–326 (2004). doi: 10.1023/B:LOGI.0000031374.60945.6e MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Wiśniewski, A.: Questions, Inferences, and Scenarios. Studies in Logic, vol. 46. College Publications, London (2013)zbMATHGoogle Scholar
  23. 23.
    Wiśniewski, A.: The Posing of Questions: Logical Foundations of Erotetic Inferences. Kluwer, Dordrecht (1995)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Logic and Cognitive Science, Institute of PsychologyAdam Mickiewicz University in PoznańPoznańPoland

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