Skip to main content
SpringerLink
Log in

Reasoning in Epistemic Contexts

  • Conference paper
  • First Online:
Modeling and Using Context (CONTEXT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10257))

  • 1034 Accesses

Abstract

In this paper, I develop a framework for representing knowledge, that aims at exploiting logically epistemological objects, namely epistemic contexts. Even though this framework is mostly logical and epistemological in character, it takes advantage of many works in artificial intelligence, in particular the ones of McCarthy and Buvač (1997). In Sect. 1, I characterize the notion of epistemic contexts. In Sect. 2, I present a natural deduction system that allows for the introduction and the elimination of knowledge operators. Such a system enables classical reasoning among contexts governed by different concepts of knowledge. Finally, in Sect. 3, I discuss some corollaries of the proposed framework (knowledge transfer, introspection, and closure).

I want to thank three anonymous referees for helpful comments on a previous version of the paper.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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.

    Description logics [1], which are used as knowledge-based representation systems, are particularly illustrative of this point. A description logic is defined by two entities, namely a terminological box (TBox) and an assertion box (ABox), that are respectively a set of declarations and a set of assertions.

  2. 2.

    For a thorough review of knowledge representation systems, see [24].

  3. 3.

    It may be interpreted more weakly as truth depending on the kind of constraints imposed on the model.

  4. 4.

    In [5], I presented a treatment of the notion of epistemic context in terms of McCarthy’s \(\texttt {ist}\) operator.

  5. 5.

    For clarifying comparisons of formal theories of context, see [6, 7, 23].

  6. 6.

    An indexical term is a term whose meaning is twofold: the first part of the meaning, the character, is an invariant part, and the second part, the content, varies in accordance with the context of use (Kaplan). Such a reading of the K-operator is typical of indexical contextualism in epistemology.

  7. 7.

    For a generalized approach allowing for differents sets of deductive schemas, see [15, 17, 19].

  8. 8.

    It is incoherent in the sense that, for example, the length of the standard meter cannot be used to measure the length of the standard meter itself.

  9. 9.

    The difference between \(\varTheta _{1}\) and \(\varTheta _{4}\) echoes the distinction between modal systems K and S5 with respect to the accessibility relation.

  10. 10.

    I am indebted to an anonymous referee for drawing my attention to this paper.

  11. 11.

    In that regard, DFOL shares some properties with labeled deduction systems (LDS) [14]. Differences between DFOL and LDS are presented in [16].

  12. 12.

    There might be some way to capture transfer rules by means of bridge rules that I am overlooking, but at this point in time it is not clear to me at all how to encode the former into the latter. A difficulty is particularly apparent in the case of second-order knowledge. For instance, assume a transfer rule such as \(KT_{1-2}: K_{1}\phi \supset K_{2}\phi \) for which \(\phi := K_{3}(p)\) in \(K_{1}\). Then, in \(K_{2}\), one would get \(K_{3}(p)\). How would this translate in terms of a bridge rule?

  13. 13.

    There is a connection in that regard with what McCarthy [21] referred to in terms of transcending contexts by means of lifting.

  14. 14.

    Among many others, see Dretske [13] (zebra argument) and DeRose [12] (argument from ignorance).

  15. 15.

    In that perspective, Dretske’s argument, which amounts to deny intracontextual closure by means of a failure of intercontextual closure, does not hold and the problematic fragment of the reasoning is made explicit in the framework.

References

  1. Baader, F., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  2. Barwise, J.: The Situation in Logic. CSLI, Stanford (1989)

    MATH  Google Scholar 

  3. van Benthem, J.: Changing contexts and shifting assertions. In: Aliseda, A., van Glabbeek, R., Westerståhl, D. (eds.) Computing Natural Language, pp. 51–65. CSLI Publications, Stanford (1998)

    Google Scholar 

  4. van Benthem, J.: McCarthy variations in a modal key. Artif. Intell. 175, 428–439 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bouchard, Y.: Epistemic contexts and indexicality. In: Lihoreau, F., Rebuschi, M. (eds.) Epistemology, Context, and Formalism, Synthese Library, vol. 369, pp. 59–79. Springer International Publishing, Cham (2014)

    Chapter  Google Scholar 

  6. Bouquet, P., Ghidini, C., Giunchiglia, F., Blanzieri, E.: Theories and uses of context in knowledge representation and reasoning. J. Pragmat. 35, 455–484 (2003)

    Article  Google Scholar 

  7. Bouquet, P., Serafini, L.: Two formalizations of context: a comparison. In: Akman, V., Bouquet, P., Thomason, R., Young, R. (eds.) CONTEXT 2001. LNCS (LNAI), vol. 2116, pp. 87–101. Springer, Heidelberg (2001). doi:10.1007/3-540-44607-9_7

    Chapter  Google Scholar 

  8. Brézillon, P.: Context in problem solving: a survey. Knowl. Eng. Rev. 14, 47–80 (1999)

    Article  MATH  Google Scholar 

  9. Buvač, S.: Resolving lexical ambiguity using a formal theory of context. In: van Deemter, K., Peters, S. (eds.) Semantic Ambiguity and Underspecification, pp. 101–124. CSLI Publications, Stanford (1996)

    Google Scholar 

  10. Buvač, S., Buvač, V., Mason, I.A.: The semantics of propositional contexts. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1994. LNCS, vol. 869, pp. 468–477. Springer, Heidelberg (1994). doi:10.1007/3-540-58495-1_47

    Chapter  Google Scholar 

  11. Buvač, S., Buvač, V., Mason, I.A.: Metamathematics of contexts. Fundam. Informaticae 23, 263–301 (1995)

    MathSciNet  MATH  Google Scholar 

  12. DeRose, K.: Solving the skeptical problem. Philos. Rev. 104, 1–52 (1995)

    Article  Google Scholar 

  13. Dretske, F.I.: Epistemic operators. J. Philos. 67, 1007–1023 (1970)

    Article  Google Scholar 

  14. Gabbay, D.M.: Labelled Deductive Systems, vol. 1. Clarendon Press, Oxford (1996)

    MATH  Google Scholar 

  15. Ghidini, C., Giunchiglia, F.: Local models semantics, or contextual reasoning=locality+compatibility. Artif. Intell. 127, 221–259 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ghidini, C., Serafini, L.: A context-based logic for distributed knowledge representation and reasoning. In: Bouquet, P., Benerecetti, M., Serafini, L., Brézillon, P., Castellani, F. (eds.) CONTEXT 1999. LNCS (LNAI), vol. 1688, pp. 159–172. Springer, Heidelberg (1999). doi:10.1007/3-540-48315-2_13

    Chapter  Google Scholar 

  17. Ghidini, C., Serafini, L.: Distributed first order logic. Computing Research Repository (CoRR) [cs.LO], pp. 1–89 (2015). arXiv:1507.07755

  18. Giunchiglia, F.: Contextual reasoning. Epistemologia 16, 341–364 (1993)

    Google Scholar 

  19. Giunchiglia, F., Serafini, L.: Multilanguage hierarchical logics, or: how we can do without modal logics. Artif. Intell. 65, 29–70 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  20. Guha, R., McCarthy, J.: Varieties of contexts. In: Blackburn, P., Ghidini, C., Turner, R.M., Giunchiglia, F. (eds.) CONTEXT 2003. LNCS (LNAI), vol. 2680, pp. 164–177. Springer, Heidelberg (2003). doi:10.1007/3-540-44958-2_14

    Chapter  Google Scholar 

  21. McCarthy, J.: Notes on formalizing context. In: Bajcsy, R. (ed.) Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI), pp. 555–560. Morgan Kaufmann, Chambéry (1993)

    Google Scholar 

  22. McCarthy, J., Buvač, S.: Formalizing context (expanded notes). In: Aliseda, A., van Glabbeek, R., Westerståhl, D. (eds.) Computing Natural Language, pp. 13–50. CSLI Publications, Stanford (1997)

    Google Scholar 

  23. Serafini, L., Bouquet, P.: Comparing formal theories of context in AI. Artif. Intell. 155, 41–67 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sowa, J.F.: Knowledge Representation. Logical, Philosophical, and Computational Foundations. Brooks/Cole, Pacific Grove (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Sherbrooke, Sherbrooke, QC, J1K2R1, Canada

    Yves Bouchard

Authors
  1. Yves Bouchard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yves Bouchard .

Editor information

Editors and Affiliations

  1. Pierre and Marie Curie University , Paris, France

    Patrick Brézillon

  2. University of Maine , Orono, Maine, USA

    Roy Turner

  3. University of Genoa , Genoa, Italy

    Carlo Penco

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Bouchard, Y. (2017). Reasoning in Epistemic Contexts. In: Brézillon, P., Turner, R., Penco, C. (eds) Modeling and Using Context. CONTEXT 2017. Lecture Notes in Computer Science(), vol 10257. Springer, Cham. https://doi.org/10.1007/978-3-319-57837-8_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-57837-8_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57836-1

  • Online ISBN: 978-3-319-57837-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation