Skip to main content

Abduction from a Dynamic Epistemic Perspective: Non-omniscient Agents and Multiagent Settings

  • Living reference work entry
  • First Online:
Handbook of Abductive Cognition

Abstract

This chapter studies abductive reasoning as an epistemic process that involves both an agent’s information and the actions that modify it. More precisely, it proposes and discusses definitions of an abductive problem and an abductive solution in terms of an agent’s information (in particular, her knowledge and beliefs) and the epistemic actions that affect it (in particular, observation and belief revision). The discussion is formalized within tools from dynamic epistemic logic, studying the properties of the given definitions, introducing an epistemic action representing the application of an abductive step, and providing illustrative examples. Two particular cases are explored: abduction for non-ideal (i.e., nonlogically omniscient) agents and abduction in multiagent scenarios.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  • Ågotnes, T., & Wáng, Y. N. (2021). Somebody knows. In M. Bienvenu, G. Lakemeyer, & E. Erdem (Eds.), Proceedings of the 18th International Conference on Principles of Knowledge Representation and Reasoning, KR 2021, Online event, 3–12 Nov 2021 (pp. 2–11).

    Google Scholar 

  • Alchourrón, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2), 510–530.

    Article  MathSciNet  MATH  Google Scholar 

  • Aliseda, A. (2000). Abduction as epistemic change: A Peircean model in artificial intelligence. In Flach and Kakas (2000) (pp. 45–58).

    Google Scholar 

  • Aliseda, A. (2003). Mathematical reasoning vs. abductive reasoning: A structural approach. Synthese, 134(1–2), 25–44.

    Article  MathSciNet  MATH  Google Scholar 

  • Aliseda, A. (2006). Abductive Reasoning. Logical Investigations into Discovery and Explanation (Synthese Library Series, Vol. 330). Springer.

    Google Scholar 

  • Baltag, A., & Smets, S. (2008). A qualitative theory of dynamic interactive belief revision. In G. Bonanno, W. van der Hoek, & M. Wooldridge (Eds.), Logic and the Foundations of Game and Decision Theory (LOFT7) (Texts in Logic and Games, Vol. 3, pp. 13–60). Amsterdam University Press.

    Google Scholar 

  • Baltag, A., & Smets, S. (2009). Learning by questions and answers: From belief-revision cycles to doxastic fixed points. In H. Ono, M. Kanazawa, & R. de Queiroz (Eds.), Logic, Language, Information and Computation (Lecture Notes in Computer Science, Vol. 5514, pp. 124–139). Berlin/Heidelberg: Springer.

    Chapter  MATH  Google Scholar 

  • Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. (Cambridge Tracts in Theoretical Computer Science, Vol. 53). Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Boutilier, C., & Becher, V. (1995). Abduction as belief revision. Artificial Intelligence, 77(1), 43–94.

    Article  MathSciNet  MATH  Google Scholar 

  • Douven, I. (2021). Abduction. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2021 edition). Metaphysics Research Lab, Stanford University.

    Google Scholar 

  • Fagin, R., & Halpern, J. Y. (1988). Belief, awareness, and limited reasoning. Artificial Intelligence, 34(1), 39–76.

    Article  MathSciNet  MATH  Google Scholar 

  • Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning About Knowledge. The MIT Press.

    MATH  Google Scholar 

  • Flach, P. A., & Kakas, A. C. (Eds.). (2000). Abduction and Induction: Essays on Their Relation and Integration (Applied Logic Series, Vol. 18). Kluwer Academic Publishers.

    Google Scholar 

  • Gerbrandy, J., & Groeneveld, W. (1997). Reasoning about information change. Journal of Logic, Language, and Information, 6(2), 147–196.

    Article  MathSciNet  MATH  Google Scholar 

  • Grossi, D., & Velázquez-Quesada, F. R. (2015). Syntactic awareness in logical dynamics. Synthese, 192(12), 4071–4105.

    Article  MathSciNet  MATH  Google Scholar 

  • Hansson, S. O. (2017). Logic of belief revision. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2017 edition). Metaphysics Research Lab, Stanford University.

    Google Scholar 

  • Harman, G. (1965). The inference to the best explanation. The Philosophical Review, 74(1), 88–95.

    Article  Google Scholar 

  • Hartshorne, C., & Weiss, P. (Eds.). (1935). Charles Sanders Peirce. The Collected Papers. Volume 5: Pragmatism and Pramaticism. Harvard University Press.

    Google Scholar 

  • Hill, B. (2010). Awareness dynamics. Journal of Philosophical Logic, 39(2), 113–137.

    Article  MathSciNet  MATH  Google Scholar 

  • Hintikka, J. (1962). Knowledge and Belief: An Introduction to the Logic of the Two Notions. Cornell University Press.

    Google Scholar 

  • Hintikka, J. (1998). What is abduction? The fundamental problem of contemporary epistemology. Transactions of the Charles S. Peirce Society, 34(3), 503–533.

    Google Scholar 

  • Jago, M. (2006). Rule-based and resource-bounded: A new look at epistemic logic. In T. Ågotnes & N. Alechina (Eds.), Proceedings of the Workshop on Logics for Resource-Bounded Agents, Organized as Part of the 18th European Summer School on Logic, Language and Information (ESSLLI) (pp. 63–77).

    Google Scholar 

  • Kakas, A. C., Kowalski, R. A., & Toni, F. (1992). Abductive logic programming. Journal of Logic and Computation, 2(6), 719–770.

    Article  MathSciNet  MATH  Google Scholar 

  • Klarman, S. (2008). Abox abduction in description logic. ILLC Master of Logic Thesis Series MoL-2008-03.

    Google Scholar 

  • Levesque, H. J. (1984). A logic of implicit and explicit belief. In R. J. Brachman (Ed.), Proceedings of AAAI-84 (pp. 198–202). AAAI Press.

    Google Scholar 

  • Levesque, H. J. (1989). A knowledge-level account of abduction. In N. S. Sridharan (Ed.), IJCAI (pp. 1061–1067). Morgan Kaufmann.

    Google Scholar 

  • Lipton, P. (2004). Inference to the Best Explanation. Routledge. First edition: 1991.

    Google Scholar 

  • Lobo, J., & Uzcátegui, C. (1997). Abductive consequence relations. Artificial Intelligence, 89 (1–2), 149–171.

    Article  MathSciNet  MATH  Google Scholar 

  • Lorini, E., & Castelfranchi, C. (2007). The cognitive structure of surprise: Looking for basic principles. Topoi, 26(1), 133–149.

    Article  MathSciNet  MATH  Google Scholar 

  • Magnani, L. (2001). Abduction, Reason, and Science: Processes of Discovery and Explanation. Springer.

    Book  Google Scholar 

  • Magnani, L. (2009). Abductive Cognition: The Epistemological and Eco-Cognitive Dimensions of Hypothetical Reasoning (Cognitive Systems Monographs, Vol. 3). Springer.

    Book  MATH  Google Scholar 

  • Mayer, M. C., & Pirri, F. (1993). First order abduction via tableau and sequent calculi. Logic Journal of the IGPL, 1(1), 99–117.

    Article  MathSciNet  MATH  Google Scholar 

  • Mayer, M. C., & Pirri, F. (1995). Propositional abduction in modal logic. Logic Journal of the IGPL, 3(6), 907–919.

    Article  MathSciNet  MATH  Google Scholar 

  • Nepomuceno-Fernández, Á., Soler-Toscano, F., & Velázquez-Quesada, F. R. (2017). Abductive reasoning in dynamic epistemic logic. In L. Magnani & T. Bertolotti (Eds.), Handbook of Model-Based Science (pp. 269–293). Springer.

    Google Scholar 

  • Park, W. (2015). On classifying abduction. Journal of Applied Logic, 13(3), 215–238.

    Article  MathSciNet  MATH  Google Scholar 

  • Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z. W. Ras (Eds.), Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems (pp. 201–216). Oak Ridge National Laboratory, ORNL/DSRD-24.

    Google Scholar 

  • Quilici-Gonzalez, M. E., & Haselager, W. P. F. G. (2005). Creativity: Surprise and abductive reasoning. Semiotica, 153(1–4), 325–342.

    Google Scholar 

  • Reyes-Cabello, A. L., Aliseda, A., & Nepomuceno-Fernández, Á. (2006). Towards abductive reasoning in first-order logic. Logic Journal of the IGPL, 14(2), 287–304.

    Article  MathSciNet  MATH  Google Scholar 

  • Rott, H. (2009). Shifting priorities: Simple representations for twenty-seven iterated theory change operators. In D. Makinson, J. Malinowski, & H. Wansing (Eds.), Towards Mathematical Philosophy (Trends in Logic, Vol. 28, pp. 269–296). Springer.

    Google Scholar 

  • Soler-Toscano, F., Fernández-Duque, D., & Nepomuceno-Fernández, Á. (2012). A modal framework for modeling abductive reasoning. Logic Journal of the IGPL, 20(2), 438–444.

    Article  MathSciNet  MATH  Google Scholar 

  • Soler-Toscano, F., & Velázquez-Quesada, F. R. (2014). Generation and selection of abductive explanations for non-omniscient agents. Journal of Logic, Language and Information, 23(2), 141–168.

    Article  MathSciNet  MATH  Google Scholar 

  • van Benthem, J. (2007). Dynamic logic for belief revision. Journal of Applied Non-Classical Logics, 17(2), 129–155.

    Article  MathSciNet  MATH  Google Scholar 

  • van Benthem, J. (2009). Abduction at the interface of logic and philosophy of science. Theoria, 22(3), 271–273.

    Google Scholar 

  • van Benthem, J. (2011). Logical Dynamics of Information and Interaction. Cambridge University Press.

    Book  MATH  Google Scholar 

  • van Benthem, J., & Velázquez-Quesada, F. R. (2010). The dynamics of awareness. Synthese (Knowledge, Rationality and Action), 177(0), 5–27.

    Google Scholar 

  • van Ditmarsch, H. (2005). Prolegomena to dynamic logic for belief revision. Synthese, 147(2), 229–275.

    Article  MathSciNet  MATH  Google Scholar 

  • van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic Epistemic Logic (Synthese Library Series, Vol. 337). Springer.

    Google Scholar 

  • Vardi, M. Y. (1986). On epistemic logic and logical omniscience. In J. Y. Halpern (Ed.), TARK (pp. 293–305). Morgan Kaufmann Publishers Inc.

    Google Scholar 

  • Velázquez-Quesada, F. R. (2014). Dynamic epistemic logic for implicit and explicit beliefs. Journal of Logic, Language and Information, 23(2), 107–140.

    Article  MathSciNet  MATH  Google Scholar 

  • Walliser, B., Zwirn, D., & Zwirn, H. (2004). Abductive logics in a belief revision framework. Journal of Logic, Language and Information, 14(1), 87–117.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Angel Nepomuceno-Fernández .

Editor information

Editors and Affiliations

Section Editor information

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Nepomuceno-Fernández, A., Soler-Toscano, F., Velázquez-Quesada, F.R. (2022). Abduction from a Dynamic Epistemic Perspective: Non-omniscient Agents and Multiagent Settings. In: Magnani, L. (eds) Handbook of Abductive Cognition. Springer, Cham. https://doi.org/10.1007/978-3-030-68436-5_25-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-68436-5_25-1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68436-5

  • Online ISBN: 978-3-030-68436-5

  • eBook Packages: Springer Reference Intelligent Technologies and RoboticsReference Module Computer Science and Engineering

Publish with us

Policies and ethics