The Calculus of Temporal Influence

Authors Florian Bruse , Marit Kastaun , Martin Lange , Sören Möller

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Author Details

Florian Bruse
  • Theoretical Computer Science / Formal Methods, University of Kassel, Germany
Marit Kastaun
  • Didactics of Biology, University of Kassel, Germany
Martin Lange
  • Theoretical Computer Science / Formal Methods, University of Kassel, Germany
Sören Möller
  • Theoretical Computer Science / Formal Methods, University of Kassel, Germany

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Florian Bruse, Marit Kastaun, Martin Lange, and Sören Möller. The Calculus of Temporal Influence. In 30th International Symposium on Temporal Representation and Reasoning (TIME 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 278, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We present the Calculus of Temporal Influence, a simple logical calculus that allows reasoning about the behaviour of real-valued functions over time by making assertions that bound their values or the values of their derivatives. The motivation for the design of such a proof system comes from the need to provide the background computational machinery for tools that support learning in experimental subjects in secondary-education classrooms. The end goal is a tool that allows school pupils to formalise hypotheses about phenomena in natural sciences, such that their validity with respect to some formal experiment model can be checked automatically. The Calculus of Temporal Influence provides a language for formal statements and the mechanisms for reasoning about valid logical consequences. It extends (and deviates in parts from) previous work introducing the Calculus of (Non-Temporal) Influence by integrating the ability to model temporal effects in such experiments. We show that reasoning in the calculus is sound with respect to a natural formal semantics, that logical consequence is at least semi-decidable, and that one obtains polynomial-time decidability for a natural stratification of the problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
  • Theory of computation → Automated reasoning
  • Applied computing → Interactive learning environments
  • temporal reasoning
  • formal models
  • continuous functions
  • polynomial decidability


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