Extensionality and intensionality of the ambient logics
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A Spatial Logic for Querying Graphs
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CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
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Pure bigraphs: Structure and dynamics
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FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
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FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
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Mathematical Structures in Computer Science
Counterpart Semantics for a Second-Order μ-Calculus
Fundamenta Informaticae - Recent Developments in the Theory of Graph Transformation, 2010
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Aiming at a unified view of the logics describing spatial structures, we introduce a general framework, BiLog, whose formulae characterise monoidal categories. As a first instance of the framework we consider bigraphs, which are emerging as a an interesting (meta-)model for spatial structures and distributed calculi. Since bigraphs are built orthogonally on two structures, a hierarchical place graph for locations and a link (hyper-)graph for connections, we obtain a logic that is a natural composition of other two instances of BiLog: a Place Graph Logic and a Link Graph Logic. We prove that these instances generalise the spatial logics for trees, for graphs and for tree contexts. We also explore the concepts of separation and sharing in these logics. We note that both the operator ∣ of Separation Logic and the operator * of spatial logics do not completely separate the underlying structures. These two different forms of separation can be naturally derived as instances of BiLog by using the complete separation induced by the tensor product of monoidal categories along with some form of sharing.