Abduction Logics: Illustrating Pitfalls of Defeasible Methods

Part of the Logic, Argumentation & Reasoning book series (LARI, volume 14)


On the one hand this paper offers an introduction to adaptive logics, focussing on properties that are imposed upon adaptive logics by the fact that they explicate defeasible reasoning. On the other hand new adaptive logics of abduction are presented and employed to illustrate those properties. These logics were developed in view of the criticism to existing adaptive logics of abduction.


Abduction Adaptive logics Defeasible reasoning 



I am indebted to Joke Meheus and especially to Frederik Van De Putte for comments on a draft of this paper.


  1. 1.
    Aliseda, A. (2006). Abductive Reasoning., Logical investigations into discovery and explanation Dordrecht: Springer.Google Scholar
  2. 2.
    Batens, D. (1980). Paraconsistent extensional propositional logics. Logique et Analyse, 90–91, 195–234.Google Scholar
  3. 3.
    Batens, D. (1989). Dynamic dialectical logics. In G. Priest, R. Routley, & J. Norman (Eds.), Paraconsistent logic (pp. 187–217)., Essays on the inconsistent München: Philosophia Verlag.Google Scholar
  4. 4.
    Batens, D. (1995). The clue to dynamic aspects of logic. Logique et Analyse, 150–152, 285–328. Appeared 1997.Google Scholar
  5. 5.
    Batens, D. (2000). Towards the unification of inconsistency handling mechanisms. Logic and Logical Philosophy, 8, 5–31. Appeared 2002.CrossRefGoogle Scholar
  6. 6.
    Batens, D. (2001). A general characterization of adaptive logics. Logique et Analyse, 173–175, 45–68. Appeared 2003.Google Scholar
  7. 7.
    Batens, D. (2004). The need for adaptive logics in epistemology. In D. Gabbay, S. Rahman, J. Symons, & J. P. V. Bendegem (Eds.), Logic (pp. 459–485)., Epistemology and the unity of science Dordrecht: Kluwer Academic Publishers.Google Scholar
  8. 8.
    Batens, D. (2005). A procedural criterion for final derivability in inconsistency-adaptive logics. Journal of Applied Logic, 3, 221–250.CrossRefGoogle Scholar
  9. 9.
    Batens, D. (2006). Narrowing down suspicion in inconsistent premise sets. In J. Malinowski & A. Pietruszczak (Eds.), Essays in Logic and Ontology (Vol. 91, pp. 185–209)., Poznań studies in the philosophy of the sciences and the humanities Amsterdam/New York: Rodopi.Google Scholar
  10. 10.
    Batens, D. (2007). A universal logic approach to adaptive logics. Logica Universalis, 1, 221–242.CrossRefGoogle Scholar
  11. 11.
    Batens, D. (2009). Towards a dialogic interpretation of dynamic proofs. In Cédric Dégremont, Laurent Keiff & Helge Rückert (Eds.), Dialogues, logics and other strange things. essays in honour of shahid rahman, (pp. 27–51). London: College Publications, 558 p.Google Scholar
  12. 12.
    Batens, D., De Clercq, K., Verdée, P., & Meheus, J. (2009). Yes fellows, most human reasoning is complex. Synthese, 166, 113–131.CrossRefGoogle Scholar
  13. 13.
    Batens, D., & Meheus, J. (2000a). The adaptive logic of compatibility. Studia Logica, 66, 327–348.Google Scholar
  14. 14.
    Batens, D., & Meheus, J. (2000b). A tableau method for inconsistency-adaptive logics. In R. Dyckhoff (Ed.), Automated Reasoning with Analytic Tableaux and Related Methods (Vol. 1847, pp. 127–142). Lecture Notes in Artificial Intelligence, Springer.Google Scholar
  15. 15.
    Batens, D., & Meheus, J. (2001). Shortcuts and dynamic marking in the tableau method for adaptive logics. Studia Logica, 69, 221–248.CrossRefGoogle Scholar
  16. 16.
    Batens, D., Straßer, C., & Verdée, P. (2009). On the transparency of defeasible logics: Equivalent premise sets, equivalence of their extensions, and maximality of the lower limit. Logique et Analyse, 207, 281–304.Google Scholar
  17. 17.
    Beirlaen, M., & Aliseda, A. (2014). A conditional logic for abduction. Synthese, 191, 3733–3758.CrossRefGoogle Scholar
  18. 18.
    Carl G. Hempel. Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. The Free Press, New York, 1965.Google Scholar
  19. 19.
    Gauderis, T. (2013). Modelling abduction in science by means of a modal adaptive logic. Foundations of Science, 18, 611–624.CrossRefGoogle Scholar
  20. 20.
    Halonen, I., & Hintikka, J. (2005). Toward a theory of the process of explanation. Synthese, 143, 5–61.CrossRefGoogle Scholar
  21. 21.
    Horsten, L., & Welch, P. (2007). The undecidability of propositional adaptive logic. Synthese, 158, 41–60.CrossRefGoogle Scholar
  22. 22.
    Leuridan, B. (2009). Causal discovery and the problem of ignorance. An adaptive logic approach. Journal of Applied Logic, 7, 188–205.CrossRefGoogle Scholar
  23. 23.
    Lewis, D. (1973). Counterfactuals. Mass.: Harvard University Press, Cambridge.Google Scholar
  24. 24.
    Lycke, H. (2012). A formal explication of the search for explanations: the adaptive logics approach to abductive reasoning. Logic Journal of the IGPL, 20, 497–516.CrossRefGoogle Scholar
  25. 25.
    Magnani, L. (2001). Abduction, reason, and science processes of discovery and explanation. New York: Kluwer Academic / Plenum Publishers.CrossRefGoogle Scholar
  26. 26.
    Magnani, L., Carnielli, W. & Pizzi, C. Eds. (2010). Model-based reasoning in science and technology. abduction, logic, and computational discovery (Vol. 314). Studies in Computational Intelligence, Heidelberg: Springer.Google Scholar
  27. 27.
    Meheus, J. (1993). Adaptive logic in scientific discovery: The case of Clausius. Logique et Analyse, 143–144, 359–389. Appeared 1996.Google Scholar
  28. 28.
    Meheus, J. (1999a). Clausius’ discovery of the first two laws of thermodynamics. A paradigm of reasoning from inconsistencies. Philosophica, 63, 89–117. Appeared 2001.Google Scholar
  29. 29.
    Meheus, J. (1999b). Deductive and ampliative adaptive logics as tools in the study of creativity. Foundations of Science, 4, 325–336.Google Scholar
  30. 30.
    Meheus, J. (1999b). Erotetic arguments from inconsistent premises. Logique et Analyse, 165–166, 49–80. Appeared 2002.Google Scholar
  31. 31.
    Meheus, J. (2001). Adaptive logics for question evocation. Logique et Analyse, 173–175, 135–164. Appeared 2003.Google Scholar
  32. 32.
    Meheus, J. (2002). Inconsistencies in scientific discovery. Clausius’s remarkable derivation of Carnot’s theorem. In H. Krach, G. Vanpaemel, & P. Marage (Eds.), History of modern physics (pp. 143–154)., Acta of the XXth International Congress of History of Science Turnhout (Belgium): Brepols.CrossRefGoogle Scholar
  33. 33.
    Meheus, J. (2011). A formal logic for the abduction of singular hypotheses. In D. Dieks, W. J. Gonzalez, S. Hartmann, T. Uebel, & M. Weber (Eds.), Explanation (pp. 93–108)., Prediction, and confirmation Dordrecht: Springer.Google Scholar
  34. 34.
    Meheus, J., Adaptive logics for abduction and the explication of explanation-seeking processes. In Pombo and Gerner [41], pp. 97–119.Google Scholar
  35. 35.
    Meheus, J., & Batens, D. (2006). A formal logic for abductive reasoning. Logic Journal of the IGPL, 14, 221–236.CrossRefGoogle Scholar
  36. 36.
    Odintsov, S. P., & Speranski, S. O. (2012). On algorithmic properties of propositional inconsistency-adaptive logics. Logic and Logical Philosophy, 21, 209–228.Google Scholar
  37. 37.
    Odintsov, S. P., & Speranski, S. O. (2013). Computability issues for adaptive logics in multi-consequence standard format. Studia Logica, 101(6), 1237–1262. doi: 10.1007/s11225-013-9531-2.CrossRefGoogle Scholar
  38. 38.
    Paul, G. (2000). AI approaches to abduction. In D. M. Gabbay & P. Smets (Eds.), Handbook of defeasible reasoning and uncertainty management systems (pp. 35–98)., Abductive reasoning and learning Dordrecht: Kluwer Academic Publishers.Google Scholar
  39. 39.
    Pogorzelski, W. A., & Prucnal, T. (1975). The substitution rule for predicate letters in the first-order predicate calculus. Reports on Mathematical Logic, 5, 77–90.Google Scholar
  40. 40.
    John, L. (1976). Pollock. Dordrecht: Subjunctive Reasoning. Reidel.Google Scholar
  41. 41.
    Pombo, O., & Gerner, A. (Eds.). (2007). Abduction and the Process of Scientific Discovery. Lisboa: Centro de Filosofia das Ciências da Universidade de Lisboa.Google Scholar
  42. 42.
    Rescher, N. (1964). Hypothetical Reasoning. Amsterdam: North-Holland.Google Scholar
  43. 43.
    Rescher, N. (1973). The Coherence Theory of Truth. Oxford: Clarendon.Google Scholar
  44. 44.
    Rescher, N. (2005). What If?. New Brunswick, New Jersey: Transaction Publishers.Google Scholar
  45. 45.
    Rescher, N., & Manor, R. (1970). On inference from inconsistent premises. Theory and Decision, 1, 179–217.CrossRefGoogle Scholar
  46. 46.
    Routley, R., & Meyer, R. K. (1976). Dialectical logic, classical logic, and the consistency of the world. Studies in Soviet Thought, 16, 1–25.CrossRefGoogle Scholar
  47. 47.
    Shapere, D. (2004). Logic and the philosophical interpretation of science. In P. Weingartner (Ed.), Alternative logics (pp. 41–54)., Do sciences need them? Berlin, Heidelberg: Springer.Google Scholar
  48. 48.
    Vanackere, G. (1997). Ambiguity-adaptive logic. Logique et Analyse, 159, 261–280. Appeared 1999.Google Scholar
  49. 49.
    Vanackere, G. (1999). Minimizing ambiguity and paraconsistency. Logique et Analyse, 165–166, 139–160. Appeared 2002.Google Scholar
  50. 50.
    Van Dyck, M. (2004). Causal discovery using adaptive logics. Towards a more realistic heuristics for human causal learning. Logique et Analyse, 185–188, 5–32. Appeared 2005.Google Scholar
  51. 51.
    Van Kerckhove, B., & Vanackere, G. (2003). Vagueness-adaptive logic: A pragmatical approach to Sorites paradoxes. Studia Logica, 75, 383–411.CrossRefGoogle Scholar
  52. 52.
    Verdée, P. (2009). Adaptive logics using the minimal abnormality strategy are \(\Pi ^1_1\)-complex. Synthese, 167, 93–104.CrossRefGoogle Scholar
  53. 53.
    Verdée, P. (2013). A proof procedure for adaptive logics. Logic Journal of the IGPL, 21, 743–766. doi: 10.1093/jigpal/jzs046.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Centre for Logic and Philosophy of ScienceGhent UniversityGhentBelgium

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