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Bringing Belief Base Change into Dynamic Epistemic Logic

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Dynamic Logic. New Trends and Applications (DALI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12005))

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Abstract

AGM’s belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been primarily used to specify the agent’s belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in dynamic epistemic logic. Particularly, it has been shown that some postulates can be characterised through transformations in priority graphs, while others may not be represented that way. This work investigates changes in the semantics of Dynamic Preference Logic that give rise to an appropriate syntactic representation for its models that allow us to represent and reason about iterated belief base change in this logic.

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Notes

  1. 1.

    The authors consider only linear models in their work and, a priori, it is not clear whether their modal equivalence result can be extended to pre-orders in general. Nevertheless, it indicates that conditionally-grounded models preserve a great deal of conditional information held in general preference models and, as such, constitute an interesting subclass of models to be studied for this logic. Our results in this work only support this conclusion by showing that, for considering this subclass of models, we can obtain interesting representation results that allow computational exploration of DPL in diverse areas.

  2. 2.

    As helpfully pointed out by one of the reviewers, since our agents are introspective in the sense that agents know about their beliefs, the belief change operations investigated in this work do change the agent’s knowledge, but only in the sense that they change their knowledge about their epistemic state, not their knowledge about the world or current state of affairs. This is an important distinction in the class of operations studied.

  3. 3.

    Other interesting examples have been previously provided by Souza et al. [31], showing that some iterated contraction operators cannot be characterised by P-graphs transformations, unless when restricted to a special class of preference models, which they call broad models.

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Authors and Affiliations

  1. Institute of Mathematics and Statistics, Federal University of Bahia - UFBA, Av. Adhemar de Barros, S/N, Ondina, Salvador, BA, Brazil

    Marlo Souza

  2. Institute of Informatics, Federal University of Rio Grande do Sul - UFRGS, Av. Bento Gonçalves, Porto Alegre, RS, 9500, Brazil

    Álvaro Moreira

Authors
  1. Marlo Souza
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  2. Álvaro Moreira
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Correspondence to Marlo Souza .

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Editors and Affiliations

  1. University of Minho, Braga, Portugal

    Luís Soares Barbosa

  2. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, Noord-Holland, The Netherlands

    Alexandru Baltag

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Souza, M., Moreira, Á. (2020). Bringing Belief Base Change into Dynamic Epistemic Logic. In: Soares Barbosa, L., Baltag, A. (eds) Dynamic Logic. New Trends and Applications. DALI 2019. Lecture Notes in Computer Science(), vol 12005. Springer, Cham. https://doi.org/10.1007/978-3-030-38808-9_12

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  • DOI: https://doi.org/10.1007/978-3-030-38808-9_12

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