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Modelling Accuracy and Trustworthiness of Explaining Agents

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 13039)


Current research in Explainable AI includes post-hoc explanation methods that focus on building transparent explaining agents able to emulate opaque ones. Such agents are naturally required to be accurate and trustworthy. However, what it means for an explaining agent to be accurate and trustworthy is far from being clear. We characterize accuracy and trustworthiness as measures of the distance between the formal properties of a given opaque system and those of its transparent explanantes. To this aim, we extend Probabilistic Computation Tree Logic with operators to specify degrees of accuracy and trustworthiness of explaining agents. We also provide a semantics for this logic, based on a multi-agent structure and relative model-checking algorithms. The paper concludes with a simple example of a possible application.


  • Explainable AI
  • Accuracy
  • Trustworthiness

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  1. 1.

    In particular, \(\sigma (\varPi )\) is usually the \(\sigma \)-algebra generated by the cylinder sets of \(\varPi \) that allows \(\sigma (\varPi )\) to be always a measurable space (see [1, 9]).

  2. 2.

    As in standard PCTL, the CTL existential and universal quantifiers, expressing quantification over paths satisfying a given formula \(\psi \), here are omitted. It is easy to prove that they correspond to special cases of probabilistic quantification. In particular, \(\exists \psi \iff P_{>0}\psi \) and \(\forall \psi \iff P_{=1}\psi \). For the details, see [1].

  3. 3.

    Notice that path-formulas \(\psi \) are usually not considered in a typical probabilistic model-checking workflow. For the details of the procedure, see [1].

  4. 4.

    Notice that, this must not be intended as a conditional probability.

  5. 5.

    Here, minimality is defined as for Eq. (2).

  6. 6.

    This represents a typical example of a stochastic machine learning model. According to the classification we propose in the introduction, it can be classified as an opaque but comprehensible model. For more details, see [2].

  7. 7.

    Remeber that an explanans is an agent able to (locally) emulate the behaviour of the target-system and usually consider more transparent than this one.

  8. 8.

    A Python implementation of Algorithm 1 is available at together with details on how to reproduce the results from the example.


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This research has been 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). The authors also thankfully acknowledge the support of the Italian Ministry of University and Research (PRIN 2017 project n. 20173YP4N3).

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Correspondence to Alberto Termine .

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Termine, A., Primiero, G., D’Asaro, F.A. (2021). Modelling Accuracy and Trustworthiness of Explaining Agents. In: Ghosh, S., Icard, T. (eds) Logic, Rationality, and Interaction. LORI 2021. Lecture Notes in Computer Science(), vol 13039. Springer, Cham.

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