A Semantical Account of Progression in the Presence of Defaults

  • Authors:

  • Gerhard Lakemeyer;Hector J. Levesque

  • Affiliations:

  • Dept. of Computer Science, RWTH, Aachen, Germany 52056;Dept. of Computer Science, University of Toronto, Toronto, Canada M5S 3A6

  • Venue:
  • Conceptual Modeling: Foundations and Applications
  • Year:
  • 2009

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Abstract

In previous work, we proposed a modal fragment of the situation calculus called ${\mathcal ES}$, which fully captures Reiter's basic action theories. ${\mathcal ES}$ also has epistemic features, including only-knowing, which refers to all that an agent knows in the sense of having a knowledge base. While our model of only-knowing has appealing properties in the static case, it appears to be problematic when actions come into play. First of all, its utility seems to be restricted to an agent's initial knowledge base. Second, while it has been shown that only-knowing correctly captures default inferences, this was only in the static case, and undesirable properties appear to arise in the presence of actions. In this paper, we remedy both of these shortcomings and propose a new dynamic semantics of only-knowing, which is closely related to Lin and Reiter's notion of progression when actions are performed and where defaults behave properly.