Graph logic (GL) is a spatial logic for querying graphs introduced by Cardelli et al. It has been observed that in terms of expressive power, this logic is a fragment of Monadic Second Order Logic (MSO), with quantification over sets of edges. We show that the containment is proper by exhibiting a property that is not GL definable but is definable in MSO, even in the absence of quantification over labels. Moreover, this holds when the graphs are restricted to be forests and thus strengthens in several ways a result of Marcinkowski. As a consequence we also obtain that Separation Logic, with a separating conjunction but without the magic wand, is strictly weaker than MSO over memory heaps, settling an open question of Brochenin et al.


  1. 1.
    Brochenin, R., Demri, S., Lozes, É.: On the almighty wand. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 323–338. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Cardelli, L., Gardner, P., Ghelli, G.: A spatial logic for querying graphs. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 597–610. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Compton, K.J.: A logical approach to asymptotic combinatorics II: Monadic second-order properties. J. Comb. Theory, Ser. A 50(1), 110–131 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Courcelle, B.: The expression of graph properties and graph transformations in monadic second-order logic. In: Rozenberg, G. (ed.) Handbook of Graph Grammars, pp. 313–400. World Scientific, Singapore (1997)Google Scholar
  5. 5.
    Dawar, A., Gardner, P., Ghelli, G.: Adjunct elimination through games in static ambient logic(Extended abstract). In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 211–223. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Dawar, A., Gardner, P., Ghelli, G.: Expressiveness and complexity of graph logic. Inf. Comput. 205(3), 263–310 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Ebbinghaus, H.-D., Flum, J.: Finite Model Theory, 2nd edn. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  8. 8.
    Grädel, E., Hirsch, C., Otto, M.: Back and forth between guarded and modal logics. ACM Trans. Comput. Log. 3(3), 418–463 (2002)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Marcinkowski, J.: On the expressive power of graph logic. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 486–500. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: LICS, pp. 55–74. IEEE Computer Society, Los Alamitos (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Timos Antonopoulos
    • 1
  • Anuj Dawar
    • 1
  1. 1.Computer LaboratoryUniversity of CambridgeCambridgeUK

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