A Probabilistic Model-Checking Framework for Cognitive Assessment and Training

Serious games have proven to be effective tools for screening cognitive impairments and supporting diagnosis in patients with neurodegenerative diseases like Alzheimer’s and Parkinson’s. They also offer cognitive training benefits. According to the DSM-5 classification, cognitive disorders are categorized as Mild Neurocognitive Disorders (mild NCDs) and Major Neurocognitive Disorders (Major NCDs). In this study, we focus on three patient groups: healthy, mild NCD, and Major NCD. We employ Discrete Time Markov Chains to model the behavior exhibited by each group while interacting with serious games. By applying model-checking techniques, we can identify discrepancies between expected and actual gameplay behavior. The primary contribution of this work is a novel theoretical framework designed to assess how a practitioner’s confidence level in diagnosing a patient’s Alzheimer’s stage evolves with each game session (diagnosis support). Additionally, we propose an experimental protocol where the difficulty of subsequent game sessions is dynamically adjusted based on the patient’s observed behavior in previous sessions (training support).

💡 Research Summary

The paper proposes a novel framework that combines serious games with probabilistic model checking to support both the assessment and training of cognitive impairments associated with neurodegenerative diseases such as Alzheimer’s and Parkinson’s. The authors focus on three patient categories defined by DSM‑5: healthy, mild neurocognitive disorder (mild NCD), and major neurocognitive disorder (Major NCD). For each category they construct a Discrete‑Time Markov Chain (DTMC) that captures the likelihood of four elementary in‑game actions: correct selection (α), incorrect selection (β), inactivity (γ), and quitting the game (θ). These DTMCs are formalized as Probabilistic Deterministic Finite Automata (PDF‑A), whose transition probabilities are initially supplied by clinicians through a questionnaire and later refined with empirical gameplay data using Bayesian updating.

The core technical contribution is a “meta‑automaton” that sits above the individual PDF‑As. Each node of the meta‑automaton corresponds to a single game session, while edges encode the transition to the next session based on the observed behavior in the current session. By employing doxastic logic, the framework quantifies the practitioner’s belief (confidence) in a particular diagnostic hypothesis and updates this belief after each session. When the confidence exceeds a predefined threshold, the diagnosis is considered stable; otherwise, additional sessions are scheduled.

Model checking is performed using Probabilistic Computation Tree Logic (PCTL) and standard tools such as PRISM. Typical properties verified include: (i) eventual reachability of a terminal state (P≥1