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Theorem Proving Using Clausal Resolution: From Past to Present

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Reachability Problems (RP 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13035))

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Abstract

Modal and temporal logics are extensions to classical logic that have operators that deal with necessity and possibility (modal logics) and such as sometime, always and next (temporal logics). Models are sets of worlds that are connected by an accessibility relation. Restrictions imposed on this relation and the operators allowed give rise to different families of logic. This paper discusses an approach to theorem proving for temporal and modal logics based on clausal resolution. The main ideas are the translation to a normal form and the application of resolution rules that relate to the same world. This research initially focused on propositional linear time temporal logic but has been extended to computation tree logic, monodic first order temporal logic and normal modal logics. We describe the approach, explain the adaptations necessary for the logics mentioned and discuss the results of the provers developed for these logics.

This work was funded by the Engineering and Physical Sciences Research Council (EPSRC) under the historic grants GR/K57282, GR/M44859 and GR/M46631 and more recently the Science of Sensor Systems Software (S4 EP/N007565/1) and by the UK Industrial Strategy Challenge Fund (ISCF), delivered by UKRI and managed by EPSRC under the grants Future AI and Robotics Hub for Space (FAIR-SPACE EP/R026092/1) and Robotics and Artificial Intelligence for Nuclear (RAIN EP/R026084/1).

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Acknowledgments

This paper describes the work of many researchers. I would like to thank all of those who collaborated to further this line of research.

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Authors and Affiliations

  1. Department of Computer Science, University of Manchester, Manchester, M13 9PL, UK

    Clare Dixon

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  1. Clare Dixon
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Correspondence to Clare Dixon .

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Editors and Affiliations

  1. Liverpool John Moores University, Liverpool, UK

    Paul C. Bell

  2. University of Liverpool, Liverpool, UK

    Patrick Totzke

  3. University of Liverpool, Liverpool, UK

    Igor Potapov

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Dixon, C. (2021). Theorem Proving Using Clausal Resolution: From Past to Present. In: Bell, P.C., Totzke, P., Potapov, I. (eds) Reachability Problems. RP 2021. Lecture Notes in Computer Science(), vol 13035. Springer, Cham. https://doi.org/10.1007/978-3-030-89716-1_2

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  • DOI: https://doi.org/10.1007/978-3-030-89716-1_2

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