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Acknowledgments We are grateful to the anonymous referees for their suggestions and remarks. We also thank Tal Lev-Ami and Greta Yorsh for their comments. References 1. edu 2. php 3. : Decidable fragments of many-sorted logic. Master’s thesis, Tel-Aviv University (2007) 4. : Verification of timed algorithms: Gurevich abstract state machines versus first order timed logic. In: Proc. of ASM 2000 International Workshop (March 2000) Decidable Fragments of Many-Sorted Logic 31 5. : Decidable verification for reducible timed automata specified in a first order logic with time.

The design and implementation of vampire. AI Communications 15(2-3), 91–110 (2002) 15. : The Z notation: a reference manual. Prentice-Hall, Englewood Cliffs (1992) 16. 42. In: CADE-13. Proceedings of the 13th International Conference on Automated Deduction, pp. 141–145. au Abstract. We give the first single-pass (“on the fly”) tableau decision procedure for computational tree logic (CTL). Our method extends Schwendimann’s single-pass decision procedure for propositional linear temporal logic (PLTL) but the extension is non-trivial because of the interactions between the branching inherent in CTL-models, which is missing in PLTL-models, and the “or” branching inherent in tableau search.

I ∈ IN. [ψ ∈ L(σi ) & ∀j < i. ϕ ∈ L(σj )]; H7 : A(ϕ U ψ) ∈ L(w) ⇒ ∀σ ∈ B(w). ∃i ∈ IN. ψ ∈ L(σi ). Although H3 captures the fix-point semantics of E(ϕ U ψ) and A(ϕ U ψ) by “locally unwinding” the fix-point, it does not guarantee a least fix-point which requires that ψ has to be true eventually. We therefore additionally need H6 and H7 which act “globally”. Note that H2 is enough to capture the correct behaviour of E(ϕ B ψ) and A(ϕ B ψ) as they have a greatest fix-point semantics. Proposition 12. A formula ϕ ∈ Fml in negation normal form is satisfiable iff there exists a Hintikka structure for ϕ.

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