Anytime, anywhere: modal logics for mobile ambients
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
BI as an assertion language for mutable data structures
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Modal logic
Separation Logic: A Logic for Shared Mutable Data Structures
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
A Semantic Basis for Local Reasoning
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
XDuce: A statically typed XML processing language
ACM Transactions on Internet Technology (TOIT)
Local reasoning for stateful programs
Local reasoning for stateful programs
TQL: a query language for semistructured data based on the ambient logic
Mathematical Structures in Computer Science
Possible worlds and resources: the semantics of BI
Theoretical Computer Science - Mathematical foundations of programming semantics
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Elimination of spatial connectives in static spatial logics
Theoretical Computer Science - Expressiveness in concurrency
Smallfoot: modular automatic assertion checking with separation logic
FMCO'05 Proceedings of the 4th international conference on Formal Methods for Components and Objects
Local Reasoning about Data Update
Electronic Notes in Theoretical Computer Science (ENTCS)
Separation Logic Semantics for Communicating Processes
Electronic Notes in Theoretical Computer Science (ENTCS)
Local Hoare reasoning about DOM
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Multimodal Separation Logic for Reasoning About Operational Semantics
Electronic Notes in Theoretical Computer Science (ENTCS)
Classical BI: a logic for reasoning about dualising resources
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Local reasoning for abstraction and sharing
Proceedings of the 2009 ACM symposium on Applied Computing
Exploring the relation between intuitionistic bi and boolean bi: An unexpected embedding
Mathematical Structures in Computer Science
Graphical models of separation logic
Information Processing Letters
Adjunct elimination in Context Logic for trees
Information and Computation
An introduction to context logic
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Adjunct elimination in context logic for trees
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
A Unified Display Proof Theory for Bunched Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Information and Computation
A marriage of rely/guarantee and separation logic
CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory
Studia Logica
Parametric completeness for separation theories
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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Separation Logic, Ambient Logic and Context Logic are based on a similar style of reasoning about structured data. They each consist of a structural (separating) composition for reasoning about disjoint subdata, and corresponding structural adjoint(s) for reasoning hypothetically about data. We show how to interpret these structural connectives as modalities in Modal Logic and prove completeness results. The structural connectives are essential for describing properties of the underlying data, such as weakest preconditions for Hoare reasoning for Separation and Context Logic, and security properties for Ambient Logic. In fact, we introduced Context Logic to reason about tree update, precisely because the structural connectives of the Ambient Logic did not have enough expressive power. Despite these connectives being essential, first Lozes then Dawar, Gardner and Ghelli proved elimination results for Separation Logic and Ambient Logic (without quantifiers). In this paper, we solve this apparent contradiction. We study parametric inexpressivity results, which demonstrate that the structural connectives are indeed fundamental for this style of reasoning.