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International Symposium on Leveraging Applications of Formal Methods

ISoLA 2018: Leveraging Applications of Formal Methods, Verification and Validation. Verification pp 28–52Cite as

Temporal Reasoning on Incomplete Paths

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11245))

Abstract

Semantics of temporal logic over truncated paths (i.e. finite paths that correspond to prefixes of computations of the system at hand) have been found useful in incomplete verification methods (such as bounded model checking and dynamic verification), in modeling hardware resets, and clock shifts and in online and offline monitoring of cyber-physical systems. In this paper we explore providing semantics for temporal logics on other types of incomplete paths, namely incomplete ultimately periodic paths, segmentally broken paths and combinations thereof. We review usages of temporal logic reasoning in systems biology, and explore whether systems biology can benefit from the suggested extensions.

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Notes

  1. 1.

    See [4] for a discussion on the difference between time-event sequences and signals, and for their algebraic representation.

  2. 2.

    There are various ways to define the semantics of the until operator in \(\text {STL}\) or \(\text {MTL}\) [39], differing in the type of closedness of the interval in which \(\varphi _1\) is required to hold. We follow the so called non-strict and non-matching variant since it is closest to the semantics of \(\text {LTL}\). It is shown in [32, 33] that this variant is as expressive as the strict variant.

  3. 3.

    These works use the traditional box and diamond notations for \(\text {LTL}\).

  4. 4.

    Formulas supported by the tool [17] use also quantification on variables and value domains. While this is not part of \(\text {LTL}\) it is part of \(\text {PSL}\) and its support is orthogonal to the use of truncated views.

  5. 5.

    Approaches that extend the set of atomic propositions with a dedicated end symbol, and require formulas to explicitily reason about it (e.g. the approach implemented in the tool RuleR [5]) suffer similar drawbacks.

  6. 6.

    Ref [10] claims some disadvantages of the three views approach to the truncated semantics, but the analysis distinguishes the weak and strong views as if they are different semantics while they are not (they are part of the same semantics with negation switching roles) and requires the next operator to be a dual of itself, while the semantics is designed so that the strong next is dual to the weak next, and strong propositions are dual to weak propositions.

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Acknowledgment

The research was partially supported by the Horizon 2020 research and innovation programme under grant agreement number 732482 (Bio4Comp).

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Authors and Affiliations

  1. Ben-Gurion University, Be’er-Sheva, Israel

    Dana Fisman

  2. Bar-Ilan University, Ramat-Gan, Israel

    Hillel Kugler

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  1. Dana Fisman
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  2. Hillel Kugler
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Correspondence to Dana Fisman or Hillel Kugler .

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Editors and Affiliations

  1. University of Limerick, Limerick, Ireland

    Tiziana Margaria

  2. TU Dortmund, Dortmund, Germany

    Bernhard Steffen

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Fisman, D., Kugler, H. (2018). Temporal Reasoning on Incomplete Paths. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation. Verification. ISoLA 2018. Lecture Notes in Computer Science(), vol 11245. Springer, Cham. https://doi.org/10.1007/978-3-030-03421-4_3

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