Contextual Modals

  • Horacio Arló Costa
  • William Taysom
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3554)


In a series of recent articles Angelika Kratzer has argued that the standard account of modality along Kripkean lines is inadequate in order to represent context-dependent modals. In particular she argued that the standard account is unable to deliver a non-trivial account of modality capable of overcoming inconsistencies of the underlying conversational background. She also emphasized the difficulties of characterizing context-dependent conditionals. As a response to these inadequacies she offered a two-dimensional account of contextual modals. Two conversational backgrounds are essentially used in this characterization of contextual modality.

We show in this paper that Kratzer’s double relative models (with finite domains) are elementary equivalent to well known neighborhood models of normal modalities originally proposed by D. Scott [S] and R. Montague [M]. We also argue that neighborhood models can be also used to represent some (non-normal) graded modalities that are difficult to represent in her framework (like ‘it is likely that’ or ‘it is highly probable that’, etc). Finally we show that an extension of the neighborhood semantics of conditionals is able to capture some of her proposals concerning dyadic modals. DR models with infinite domains can be shown to be pointwise equivalent to neighborhood models, but they are not guaranteed to have relational counterparts. So DR models surpass the representational power of relational (Kripkean) models. Neighborhood representations are, nevertheless, always possible, making clear as well that the central feature of double relative modals is that they are capable of encoding two central aspects of context: its propositional content, and its dynamic properties (which in Kratzer’s models are represented via an ordering source).


Modal Logic Minimal Model Modal Base Standard Account Contextual Modal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AC]
    Arlo Costa, H.: First order extensions of classical systems of modal logic: The role of the Barcan schemas. Studia Logica 71, 87–118 (forthcoming 2002)zbMATHCrossRefMathSciNetGoogle Scholar
  2. [HAC]
    Arlo Costa, H., Pacuit, E.: First order classical modal logic. Technical Report No. CMU-PHIL-164, Carnegie Mellon University (2004); An abbreviated version is forthcoming in TARK XGoogle Scholar
  3. [Ben]
    Ben-David, S., Ben-Eliyahu, R.: A Modal Logic for Subjective Default Reasoning. Artificial Intelligence 116, 217–236 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. [Ch]
    Chellas, B.: Modal logic: An introduction. Cambridge UP, Cambridge (1980)zbMATHGoogle Scholar
  5. [K]
    Kratzer, A.: Modality. In: von Stechow, A., Wunderlich, D. (eds.) Semantik. Ein internationales Handbuch der zeitgenossischen Forschung, Walter de Gruyter, Berlin, pp. 639–650 (1991)Google Scholar
  6. [K2]
    Kratzer, A.: What ’must’ and ’can’ must and can mean. Linguistics and Philosophy 1(3), 337–356 (1977)CrossRefGoogle Scholar
  7. [Le]
    Levi, I.: For the sake of the argument: Ramsey test conditionals, Inductive Inference, and Nonmonotonic reasoning. Cambridge University Press, Cambridge (1996)zbMATHCrossRefGoogle Scholar
  8. [L]
    Lewis, D.: Counterfactuals. Blackwell, Malden (1973)Google Scholar
  9. [M]
    Montague, R.: Pragmatics. Contemporary Philosophy, La Nuova Italia Editrice, 101–121 (1968)Google Scholar
  10. [Sen]
    Sen, A.: Non-Binary Choice and Preference. In: Rationality and Freedom. Harvard University Press, Cambridge (2003)Google Scholar
  11. [S]
    Scott, D.: Advice on modal logic. Philosophical Problems in Logic, 143–173 (1970)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Horacio Arló Costa
    • 1
  • William Taysom
    • 2
  1. 1.Carnegie Mellon University 
  2. 2.Institute for Human and Machine Cognition 

Personalised recommendations