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Deciding validity in a spatial logic for trees

  • CRISTIANO CALCAGNO (a1), LUCA CARDELLI (a2) and ANDREW D. GORDON (a2)
Abstract

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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Journal of Functional Programming
  • ISSN: 0956-7968
  • EISSN: 1469-7653
  • URL: /core/journals/journal-of-functional-programming
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