, Volume 26, Issue 1, pp 37–49 | Cite as

Abductive reasoning in neural-symbolic systems

  • Artur S. d’Avila Garcez
  • Dov M. Gabbay
  • Oliver Ray
  • John Woods
Original paper


Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration.


Abduction Abductive logic programming Connectionist modal logic Neural networks 



We are grateful to Wilfrid Hodges, Johan van Benthem, and two anonymous referees for their valuable comments, which have helped improve this paper.


  1. Aiello A, Burattini E, Tamburrini G (1995) Purely neural, rule-based diagnostic systems II: Uncertain reasoning. Int J Intelligent Syst 10:751–769Google Scholar
  2. Ayeb B, Wang S, Ge J (1998) A unified model for neural based abduction. IEEE Trans Syst Man Cybernet 28(4):408–425CrossRefGoogle Scholar
  3. Bylander T, Allemang D, Tanner MC, Josephson JR (1991) The computational complexity of abduction. Artif Intell 49:25–60CrossRefGoogle Scholar
  4. Charniak E, McDermott D (eds) (1985) Introduction to artificial intelligence. Addison-Wesley, Reading MAGoogle Scholar
  5. Churchland P (1989) A neurocomputational perspective: the nature of mind and the structure of science. MIT Press, Cambridge MAGoogle Scholar
  6. d’Avila Garcez AS, Broda K, Gabbay D (2002) Neural-symbolic learning systems: foundations and applications. Perspectives in neural computing. Springer-VerlagGoogle Scholar
  7. d’Avila Garcez AS, Lamb LC, Broda K, Gabbay DM (2004) Applying connectionist modal logics to distributed knowledge representation problems. Int J Artificial Intell Tools 13(1):115–139CrossRefGoogle Scholar
  8. d’Avila Garcez AS, Lamb LC, Gabbay DM (2006a). Connectionist computations of intuitionistic reasoning. Theoret Comput Sci 358(1):34–55CrossRefGoogle Scholar
  9. d’Avila Garcez AS, Lamb LC, Gabbay DM (2006b) Connectionist modal logic. Theoret Comput Sci  doi:10.1016/j.tcs.2006.10.023
  10. Flach P, Kakas A (ed) (2000) Abduction and induction: essays on their relation and integration, vol 18 of applied logic series. KluwerGoogle Scholar
  11. Gabbay D, Woods J (2005) The reach of abduction: insight and trial. ElsevierGoogle Scholar
  12. Goel A, Ramanujam J (1996) A neural architecture for a class of abduction problems. IEEE Trans Syst, Man Cybernet 26(6):854–860CrossRefGoogle Scholar
  13. Hobbs JR, Stickel ME, Appelt DE, Martin P (1993) Interpretation as abduction. Artif Intell 63(1–2):69–142CrossRefGoogle Scholar
  14. Hughes GE, Cresswell MJ (1996) A new introduction to modal logic. Routledge, London and New YorkGoogle Scholar
  15. Inoue K (2001) Induction, abduction, and consequence-finding. In: Rouveirol C, Sebag M (eds) Proceedings 11th International Conference on Inductive Logic Programming, vol 2157 of Lecture Notes in Artificial Intelligence. Springer Verlag, pp 65–79Google Scholar
  16. Josephson JR, Josephson SG (eds) (1994) Abductive inference: computation, philosophy, technology. Cambridge University PressGoogle Scholar
  17. Kakas A, Kowalski R, Toni F (1992) Abductive logic programming. J Logic Comput 2(6):719–770CrossRefGoogle Scholar
  18. Kakas AC, Kowalski RA, Toni F (1994) The role of abduction in logic programming. In: Gabbay DM, Hogger C, Robinson JA (eds) Handbook of logic in artificial intelligence and logic programming, vol 5. Oxford Science Publications, pp 235–324Google Scholar
  19. Levesque H (1989) A knowledge-level account of abduction. In: Proceedings of international joint conference on artificial intelligence, IJCAI’89, vol 2, pp 1061–1067Google Scholar
  20. Lloyd J (1987) Foundations of logic programming. Springer VerlagGoogle Scholar
  21. Magnani L (ed) (2001) Abduction, reason, and science. Processes of discovery and explanation. Kluwer Academic/Plenum Publishers, New YorkGoogle Scholar
  22. Michalski R (1993) Inferential theory of learning: developing foundations for multistrategy learning. In: Michalski R, Tecuci G (eds) Machine learning: a multistrategy approach. Morgan KaufmannGoogle Scholar
  23. Orgun MA, Ma W (1994) An overview of temporal and modal logic programming. In: Proceedings of international conference on temporal logic, LNAI 827. Springer, pp 445–479Google Scholar
  24. Page M (2000) Connectionist modelling in psychology: a localist manifesto. Behav Brain Sci 23:443–467CrossRefGoogle Scholar
  25. Perkins DN (2000) The eureka effect: the art and science of breakthrough thinking. Norton, New YorkGoogle Scholar
  26. Ray O (2005) Hybrid abductive inductive learning. PhD thesis, Department of Computing, Imperial College LondonGoogle Scholar
  27. Ray O, d’Avila Garcez AS (2006) Towards the integration of abduction and induction in artificial neural networks. In: Proceedings of 2nd international workshop on neural-symbolic learning and reasoning, Riva del GardaGoogle Scholar
  28. Ray O, Kakas A (2006) ProLogICA: a practical system for abductive logic programming. In: Proceedings of the 11th international workshop on non-monotonic reasoning, Lake DistrictGoogle Scholar
  29. Reggia J, Peng Y, Tuhrim S (1993) A connectionist approach to diagnostic problem-solving using causal networks. Inform Sci 70:27–48CrossRefGoogle Scholar
  30. Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal representations by error propagation. In: Rumelhart DE, McClelland JL (eds) Parallel distributed processing: explorations in the microstructure of cognition, vol 1. MIT Press, pp 318–362Google Scholar
  31. Sejnowski T, Abbott L (eds) (1999) Neural codes and distributed representations: foundations of neural computation. MIT PressGoogle Scholar
  32. Shastri L, Ajjanagadde V (1993) From associations to systematic reasoning: a connectionist representation of rules, variables and dynamic bindings using temporal synchrony. Behav Brain Sci 16(3):417–494CrossRefGoogle Scholar
  33. Simons P, Niemelä I, Soininen T (2002) Extending and implementing the stable model semantics. Artif Intell 138(1–2):181–234CrossRefGoogle Scholar
  34. Smolensky P (2000) Grammar-based connectionist approaches to language. Cognitive Sci 23:589–613CrossRefGoogle Scholar
  35. Smolensky P, Legendre G (2006) The harmonic mind: from neural computation to optimality-theoretic grammar. MIT Press, Cambridge MassGoogle Scholar
  36. Sun R (1995) Robust reasoning: integrating rule-based and similarity-based reasoning. Artif Intell 75(2):241–296CrossRefGoogle Scholar
  37. Thaggard P (1989) Explanatory coherence. Behav Brain Sci 12:435–502Google Scholar
  38. Towell GG, Shavlik JW (1994) Knowledge-based artificial neural networks. Artif Intell 70(1):119–165CrossRefGoogle Scholar
  39. Wang H, Johnson TR, Zhang J (2006) A hybrid system of abductive tactical decision making. Int J Hybrid Intell Syst 3(1):23–33Google Scholar
  40. Weber RJ, Perkins DN (eds) (1992) Inventive minds: creativity and technology. Oxford University Press, New York and OxfordGoogle Scholar
  41. Zhang C, Xu Y (1999). A neural network model for diagnostic problem solving with causal chaining. Neural Networks Adv Control Strategies 54:87–92Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Artur S. d’Avila Garcez
    • 1
  • Dov M. Gabbay
    • 2
  • Oliver Ray
    • 3
  • John Woods
    • 4
  1. 1.Department of ComputingCity University LondonLondonUK
  2. 2.Department of Computer ScienceKing’s College LondonLondonUK
  3. 3.Department of ComputingImperial College LondonLondonUK
  4. 4.Department of PhilosophyUniversity of British ColumbiaVancouverCanada

Personalised recommendations