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A Cyclic Proof System for Full Computation Tree Logic

Authors Bahareh Afshari, Graham E. Leigh, Guillermo Menéndez Turata

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Author Details

Bahareh Afshari
  • Institute for Logic, Language and Computation, University of Amsterdam, The Netherlands
  • Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg, Sweden
Graham E. Leigh
  • Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg, Sweden
Guillermo Menéndez Turata
  • Institute for Logic, Language and Computation, University of Amsterdam, The Netherlands

Funding

Supported by the Knut and Alice Wallenberg Foundation [2020.0199]; Swedish Research Council [2017-05111, 2016-03502]; and the Dutch Research Council [OCENW.M20.048].

Cite As Get BibTex

Bahareh Afshari, Graham E. Leigh, and Guillermo Menéndez Turata. A Cyclic Proof System for Full Computation Tree Logic. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CSL.2023.5

Abstract

Full Computation Tree Logic, commonly denoted CTL*, is the extension of Linear Temporal Logic LTL by path quantification for reasoning about branching time. In contrast to traditional Computation Tree Logic CTL, the path quantifiers are not bound to specific linear modalities, resulting in a more expressive language. We present a sound and complete hypersequent calculus for CTL*. The proof system is cyclic in the sense that proofs are finite derivation trees with back-edges. A syntactic success condition on non-axiomatic leaves guarantees soundness. Completeness is established by relating cyclic proofs to a natural ill-founded sequent calculus for the logic.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Proof theory
Keywords
  • Full computation tree logic
  • Hypersequent calculus
  • Cyclic proofs

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