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Deciding validity in a spatial logic for trees

Published online by Cambridge University Press:  05 January 2005

CRISTIANO CALCAGNO
Affiliation:
Imperial College London, London, UK (e-mail: ccris@doc.ic.ac.uk)
LUCA CARDELLI
Affiliation:
Microsoft Research, Cambridge, UK
ANDREW D. GORDON
Affiliation:
Microsoft Research, Cambridge, UK
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Abstract

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We consider a propositional spatial logic for finite trees. The logic includes $\A \Par \B$ (tree composition), $\A \,{\Guarantee}\, \B$ (the implication induced by composition), and $\Zero$ (the unit of composition). We show that the satisfaction and validity problems are equivalent, and decidable. The crux of the argument is devising a finite enumeration of trees to consider when deciding whether a spatial implication is satisfied. We introduce a sequent calculus for the logic, and show it to be sound and complete with respect to an interpretation in terms of satisfaction. Finally, we describe a complete proof procedure for the sequent calculus. We envisage applications in the area of logic-based type systems for semistructured data. We describe a small programming language based on this idea.

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Article
Copyright
© 2005 Cambridge University Press
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