Foundations of Inconsistency-Tolerant Model Checking: Logics, Translations, and Examples

  • Norihiro KamideEmail author
  • Kazuki Endo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11352)


We develop logics and translations for inconsistency-tolerant model checking that can be used to verify systems having inconsistencies. Paraconsistent linear-time temporal logic (pLTL), paraconsistent computation tree logic (pCTL), and paraconsistent full computation tree logic (pCTL\(^*\)) are introduced. These are extensions of standard linear-time temporal logic (LTL), standard computation tree logic (CTL), and standard full computation tree logic (CTL\(^*\)), respectively. These novel logics can be applied when handling inconsistency-tolerant temporal reasoning. They are also regarded as four-valued temporal logics that extend Belnap and Dunn’s four-valued logic. Translations from pLTL into LTL, pCTL into CTL, and pCTL\(^*\) into CTL\(^*\), are defined, and these are used to prove the theorems for embedding pLTL into LTL, pCTL into CTL, and pCTL\(^*\) into CTL\(^*\). These embedding theorems allow the standard LTL-, CTL-, and CTL\(^*\)-based model checking algorithms to be used for verifying inconsistent systems that are modeled and specified by pLTL, pCTL, and pCTL\(^*\). Some illustrative examples for inconsistency-tolerant model checking are presented based on the proposed logics and translations.



This research was supported by JSPS KAKENHI Grant Numbers JP16KK0007 and JP18K11171. This research has been supported by the Kayamori Foundation of Informational Science Advancement and JSPS Core-to-Core Program (A. Advanced Research Networks).


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Authors and Affiliations

  1. 1.Faculty of Science and Engineering, Department of Information and Electronic EngineeringTeikyo UniversityUtsunomiyaJapan
  2. 2.Faculty of Science and Engineering, Department of Human Information SystemsTeikyo UniversityUtsunomiya-shiJapan

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