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Decidability Borders of Verification of Communicating Datalog Agents

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Multi-Agent Systems (EUMAS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14282))

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Abstract

We present our recent results in charting the decidability boundary of formal verification of Communicating Datalog Agents, a multi-agent system grounded in logic programming.

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Notes

  1. 1.

    A signature \(\mathcal {A}\) is a finite set \(\{A_1/{a_1},\dots ,A_n/{a_n}\}\) where, for \(i\in \{1,\dots ,n\}\), \(A_i\) is a symbol and \(a_i\in \mathbb {N}\) is its arity. Given a countably infinite set \(\varDelta \), called domain, of constants, a fact over \(\mathcal {A}\) is a formula \(A_i(c_1,\dots ,c_{a_i})\), where \(c_J\in \varDelta \) for each \(J\in \{1,\dots ,a_i\}\). A DB over \(\mathcal {A}\) is a finite set of facts over \(\mathcal {A}\).

  2. 2.

    Notice that agent names are considered constants in \(\varDelta \) and can appear in facts.

  3. 3.

    Notice that reactions to changes in the information provided by the environment can still be modeled by sending on the self-loop channel a dedicated message.

  4. 4.

    In case of ordered channels, the outgoing messages are sent in non-deterministic order. This way, only the order among the messages sent at different steps is relevant. While more sophisticated casting policies may be enforced, their relevance is limited, since ordered channels cause almost immediately undecidable verification [8].

  5. 5.

    Fixed a countably infinite set \(\mathcal {V}\) of variables, such that \(\varDelta \cap \mathcal {V}=\emptyset \), a term is a constant or a variable. An atom over \(\mathcal {A}\) is a formula \(A(t_1,\dots ,t_{a})\) such that \(A/a\in \mathcal {A}\) and, for each \(i\in \{1,\dots ,a\}\), \(t_i\) is a term. A positive literal over \(\mathcal {A}\) is an atom \(\varphi \) over \(\mathcal {A}\). A negative literal over \(\mathcal {A}\) is a formula \(\textbf{not}~\varphi \), where \(\varphi \) is an atom over \(\mathcal {A}\).

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Author information

Authors and Affiliations

  1. Free University of Bozen-Bolzano, Bolzano, Italy

    Francesco Di Cosmo

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  1. Francesco Di Cosmo
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Correspondence to Francesco Di Cosmo .

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Editors and Affiliations

  1. Télécom Paris, Paris, France

    Vadim Malvone

  2. Universitá degli Studi di Napoli Federico II, Naples, Italy

    Aniello Murano

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Di Cosmo, F. (2023). Decidability Borders of Verification of Communicating Datalog Agents. In: Malvone, V., Murano, A. (eds) Multi-Agent Systems. EUMAS 2023. Lecture Notes in Computer Science(), vol 14282. Springer, Cham. https://doi.org/10.1007/978-3-031-43264-4_39

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  • DOI: https://doi.org/10.1007/978-3-031-43264-4_39

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