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Static BiLog: a Unifying Language for Spatial Structures

Static BiLog: a Unifying Language for Spatial Structures
Static BiLog: a Unifying Language for Spatial Structures
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.
Concurrency, Bigraphs, Spatial Logics, Context Logic, Separation, XML
1-20
Conforti, G.
6d02581e-7add-4f16-a1e5-841c88e6b2e2
Macedonio, D.
fd742c8a-820c-4ad2-a72a-94c44171917f
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7
Conforti, G.
6d02581e-7add-4f16-a1e5-841c88e6b2e2
Macedonio, D.
fd742c8a-820c-4ad2-a72a-94c44171917f
Sassone, V.
df7d3c83-2aa0-4571-be94-9473b07b03e7

Conforti, G., Macedonio, D. and Sassone, V. (2007) Static BiLog: a Unifying Language for Spatial Structures. Fundamenta Informaticae, 80, 1-20.

Record type: Article

Abstract

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.

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Published date: July 2007
Keywords: Concurrency, Bigraphs, Spatial Logics, Context Logic, Separation, XML
Organisations: Web & Internet Science

Identifiers

Local EPrints ID: 264902
URI: http://eprints.soton.ac.uk/id/eprint/264902
PURE UUID: debd3850-263c-411a-a051-33f876810e52

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Date deposited: 27 Nov 2007 13:52
Last modified: 28 Oct 2019 21:22

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