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Operational Causality – Necessarily Sufficient and Sufficiently Necessary

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A Journey from Process Algebra via Timed Automata to Model Learning

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13560))

Abstract

Necessity and sufficiency are well-established notions in logic and causality analysis, but have barely received attention in the formal methods community. In this paper, we present temporal logic characterizations of necessary and sufficient causes in terms of state sets in operational system models. We introduce degrees of necessity and sufficiency as quality measures for sufficient and necessary causes, respectively, along with a versatile weight-based approach to find “good causes”. The resulting optimization problems of finding optimal causes are shown to be solvable in polynomial time.

The authors are supported by the DFG through the Collaborative Research Center TRR 248 (CPEC, project ID 389792660, https://perspicuous-computing.science), the Cluster of Excellence EXC 2050/1 (CeTI, project ID 390696704, as part of Germany’s Excellence Strategy) and the Research Training Groups QuantLA (GRK 1763) and RoSI (GRK 1907).

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Notes

  1. 1.

    The problem of finding balanced vertex separators, as studied by Feige et al. [27, 28], is NP-complete and differs from the one we study in that it requires that the vertex separator partitions the graph into approximately equally sized components.

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Authors and Affiliations

  1. Technische Universität Dresden, Dresden, Germany

    Christel Baier, Clemens Dubslaff, Florian Funke, Simon Jantsch, Jakob Piribauer & Robin Ziemek

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  1. Christel Baier
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  2. Clemens Dubslaff
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  3. Florian Funke
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Correspondence to Christel Baier , Clemens Dubslaff , Florian Funke , Simon Jantsch , Jakob Piribauer or Robin Ziemek .

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  1. Radboud University Nijmegen, Nijmegen, The Netherlands

    Nils Jansen

  2. University of Twente, Enschede, The Netherlands

    Mariëlle Stoelinga

  3. University of Twente, Enschede, The Netherlands

    Petra van den Bos

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Baier, C., Dubslaff, C., Funke, F., Jantsch, S., Piribauer, J., Ziemek, R. (2022). Operational Causality – Necessarily Sufficient and Sufficiently Necessary. In: Jansen, N., Stoelinga, M., van den Bos, P. (eds) A Journey from Process Algebra via Timed Automata to Model Learning . Lecture Notes in Computer Science, vol 13560. Springer, Cham. https://doi.org/10.1007/978-3-031-15629-8_2

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