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Doxastic Group Reasoning via Multiple Belief Shadowing

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PRIMA 2019: Principles and Practice of Multi-Agent Systems (PRIMA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11873))


In real world situations an agent may need to switch between distinct roles and/or groups. This calls for a well-controlled and computationally-friendly adjustment of relevant beliefs, especially when groups’ structures and organization evolve dynamically. A need for adaptability may also emerge from the impossibility of fixing agents’ roles or teams at design time. In such changing circumstances reasoning about beliefs is a challenging issue.

A concept of belief shadowing, introduced in [8], address these phenomena with a use of \(A {} \texttt {a}{} \texttt {s}B\) operator expressing that A acts as B. That is, beliefs of \(A {} \texttt {a}{} \texttt {s}B\) are those of B, unless B does not know the doxastic status of a given belief, in which case the belief of A is binding. This simple construct turns out to be efficient for shallow and transient forms of belief change. Yet, while being convenient in situations when an agent plays a specific role or joins a given group, single shadowing hardly fits cases of multiple roles and/or multiple groups entered simultaneously without prioritizing them. As a remedy we introduce multiple shadowing together with a query language, , where roles and groups are dealt with uniformly.

The multiple shadowing operator appears simple yet flexible for reasoning about the associated beliefs, which otherwise are rather complex and onerous to reason about.Importantly, the presented language is tractable. Possible applications of  as a lightweight tool for doxastic reasoning are pointed out.

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  1. 1.

    Note, however, that the semantics of the language will be non-classical.

  2. 2.

    Of course, the multiplicity of testimonies could be useful in disambiguating potential inconsistencies. Here, for simplicity, we use sets, but multisets could be represented by adding integer parameter specifying the number of persons testifying a given fact.

  3. 3.

    For the sake of simplicity \(\lnot \lnot \ell \) is identified with \(\ell \).

  4. 4.

    Evidence gathering proceeds bottom up: from the lack of information to false or true, and perhaps finally to inconsistency.

  5. 5.

    The argument w is irrelevant here: \(\mathrm {Bel}{[]}\big (\big )\) applies to belief bases rather than to worlds.

  6. 6.

    That way flexible constraints of \(\varDelta _1\) are relaxed.

  7. 7.

    Questions on how to prioritize the groups as well as how to handle inconsistent rigid constraints are out of the scope of this work.

  8. 8.

    The time is logarithmic on a polynomially bounded number of processors running in parallel.

  9. 9.

    This calls for computing \(\varGamma '\) using the epistemic profile of G with the new set of agents, using their belief bases \(\varDelta _1,\ldots ,\varDelta _s\).


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The research reported in this paper has been supported by the Polish National Science Centre grant 2015/19/B/ST6/02589, the ELLIIT network organization for Information and Communication Technology, and the Swedish Foundation for Strategic Research FSR (SymbiKBot Project).

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Correspondence to Andrzej Szałas .

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Dunin-Kęplicz, B., Rüb, I., Szałas, A. (2019). Doxastic Group Reasoning via Multiple Belief Shadowing. In: Baldoni, M., Dastani, M., Liao, B., Sakurai, Y., Zalila Wenkstern, R. (eds) PRIMA 2019: Principles and Practice of Multi-Agent Systems. PRIMA 2019. Lecture Notes in Computer Science(), vol 11873. Springer, Cham.

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