A Temporal Logic for Modelling Activities of Daily Living

Authors Malte S. Kließ , Catholijn M. Jonker , M. Birna van Riemsdijk

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Malte S. Kließ
  • Interactive Intelligence, Delft University of Technology, Delft, The Netherlands
Catholijn M. Jonker
  • Interactive Intelligence, Delft University of Technology, Delft, The Netherlands and , Leiden Institute of Advanced Computer Science, Leiden University
M. Birna van Riemsdijk
  • Interactive Intelligence, Delft University of Technology, Delft, The Netherlands

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Malte S. Kließ, Catholijn M. Jonker, and M. Birna van Riemsdijk. A Temporal Logic for Modelling Activities of Daily Living. In 25th International Symposium on Temporal Representation and Reasoning (TIME 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 120, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Behaviour support technology is aimed at assisting people in organizing their Activities of Daily Living (ADLs). Numerous frameworks have been developed for activity recognition and for generating specific types of support actions, such as reminders. The main goal of our research is to develop a generic formal framework for representing and reasoning about ADLs and their temporal relations. This framework should facilitate modelling and reasoning about 1) durative activities, 2) relations between higher-level activities and subactivities, 3) activity instances, and 4) activity duration. In this paper we present a temporal logic as an extension of the logic TPTL for specification of real-time systems. Our logic TPTL_{bih} is defined over Behaviour Identification Hierarchies (BIHs) for representing ADL structure and typical activity duration. To model execution of ADLs, states of the temporal traces in TPTL_{bih} comprise information about the start, stop and current execution of activities. We provide a number of constraints on these traces that we stipulate are desired for the accurate representation of ADL execution, and investigate corresponding validities in the logic. To evaluate the expressivity of the logic, we give a formal definition for the notion of Coherence for (complex) activities, by which we mean that an activity is done without interruption and in a timely fashion. We show that the definition is satisfiable in our framework. In this way the logic forms the basis for a generic monitoring and reasoning framework for ADLs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Temporal Logic
  • Reasoning
  • Durative Activities


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