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A Multi-Agent Depth Bounded Boolean Logic

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Book cover Software Engineering and Formal Methods. SEFM 2020 Collocated Workshops (SEFM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12524))

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Abstract

Recent developments in the formalization of reasoning, especially in computational settings, have aimed at defining cognitive and resource bounds to express limited inferential abilities. This feature is emphasized by Depth Bounded Boolean Logics, an informational logic that models epistemic agents with inferential abilities bounded by the amount of information they can use. However, such logics do not model the ability of agents to make use of information shared by other sources. The present paper provides a first account of a Multi-Agent Depth Bounded Boolean Logic, defining agents whose limited inferential abilities can be increased through a dynamic operation of becoming informed by other data sources.

This research was funded by the Department of Philosophy “Piero Martinetti” of the University of Milan under the project “Departments of Excellence 2018–2022” awarded by the Ministry of Education, University and Research (MIUR); and supported by the Austrian Science Fund (FWF) project ByzDEL (P33600). The authors wish to thank Marcello D’Agostino and Pere Pardo for comments on previous versions of this work.

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Notes

  1. 1.

    We use here a two-value valuation function v on formulas as a mapping to truth and falsity. Its formal definition, extended to a three-valued function, is postponed to Sect. 3.

  2. 2.

    This example is based on an unpublished one formulated by Marcello D’Agostino.

  3. 3.

    The two operators reflect the distinction between an alethically neutral and a veridical conception of information, see [17] and [11] respectively. Technically, it is possible to reformulate the present monotonic version of MA-DBBL without the I operator without loss of expressiveness. We keep it both in the language to preserve the mentioned conceptual distinction, and because it offers the basis for a planned extension of the present system with contradictory information updates.

  4. 4.

    We stress here that while in single agent DBBL the depth of the reasoning process is given by nested applications of RB by the agent, in MA-DBBL are the instances of RB indexed by distinct agents that determine such depth.

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Authors and Affiliations

  1. Embedded Computing Systems, TU Wien, Vienna, Austria

    Giorgio Cignarale

  2. Department of Philosophy, University of Milan, Milan, Italy

    Giuseppe Primiero

Authors
  1. Giorgio Cignarale
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  2. Giuseppe Primiero
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Correspondence to Giorgio Cignarale .

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Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Loek Cleophas

  2. CNR-ISTI, Pisa, Italy

    Mieke Massink

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Cignarale, G., Primiero, G. (2021). A Multi-Agent Depth Bounded Boolean Logic. In: Cleophas, L., Massink, M. (eds) Software Engineering and Formal Methods. SEFM 2020 Collocated Workshops. SEFM 2020. Lecture Notes in Computer Science(), vol 12524. Springer, Cham. https://doi.org/10.1007/978-3-030-67220-1_14

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  • DOI: https://doi.org/10.1007/978-3-030-67220-1_14

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