## Spatial Logics for Bigraphs (2005)

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Venue: | In Proceedings of ICALP’05, volume 3580 of LNCS |

Citations: | 21 - 2 self |

### BibTeX

@INPROCEEDINGS{Conforti05spatiallogics,

author = {Giovanni Conforti and Damiano Macedonio and Vladimiro Sassone},

title = {Spatial Logics for Bigraphs},

booktitle = {In Proceedings of ICALP’05, volume 3580 of LNCS},

year = {2005},

pages = {766--778},

publisher = {Springer-Verlag}

}

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### Abstract

Abstract. Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts. 1

### Citations

269 | Local reasoning about programs that alter data structures
- O’Hearn, Reynolds, et al.
- 2001
(Show Context)
Citation Context ...plits a term into two parts, in order to ‘talk’ about them separately. Looking closely, we observe that the notion of separation is interpreted differently in different logics. In ‘separation’ logics =-=[18]-=-, it is used to reason about dynamic update of heap-like structures, and it is strong in that it forces names of resources in separated components to be disjoint. As a consequence, term composition is... |

162 | Anytime, anywhere. Modal logics for mobile ambients
- Cardelli, Gordon
- 2000
(Show Context)
Citation Context ...espond to quantifications on the horizontal/vertical structure of terms. The equality between interfaces I = J is easily derivable using ⊗ and ⊗−. We can extend the idea of sublocation (⊑) defined in =-=[7]-=- to our terms. The inductive definition of ⊑ specifies that G ⊑ G, and G ′ ⊑ G if either G ≡ G1 ⊗ G2, with G ′ ⊑ G1 (and symmetrically G ′ ⊑ G2) or G ≡ G1 ◦ G2, with τ(G1) and G ′ ⊑ G2. Exploiting thi... |

162 | Nominal Logic, A first order theory of names and binding
- Pitts
(Show Context)
Citation Context ...ld formulae that explore a link, since the latter has the effect of hiding names. For this task, we employ the name variables x1, ..., xn and a fresh name quantification in the style of Nominal Logic =-=[19]-=-. G |=N x1, . . . , xn. A def = ∃a1 . . . an � fn(G) ∪ fn(A). G |= A{x1, . . . xn ← a1 . . . an} Using fresh name quantification we can define a notion of �a-linked name quantification for fresh names... |

136 | A spatial logic for concurrency (part I
- Caires, Cardelli
- 2001
(Show Context)
Citation Context ..., the separation/composition does not require any constraint on terms, and names are usually shared between separated parts. Similarly in dynamic spatial logics (for, e.g., ambients [6] or π-calculus =-=[1]-=-), where the separation is intended only for location in space. Context tree logic, introduced in [3], integrates the first approach above with a spatial logic for trees. The result is a logic able to... |

63 |
2001): Bigraphical Reactive Systems
- Milner
(Show Context)
Citation Context ...logic able to express properties of treeshaped structures (and contexts) with pointers, and it is used as an assertion language for Hoare-style program specifications in a tree memory model. Bigraphs =-=[12, 14]-=- are an emerging model for structures in global computing, which can be instantiated to model several well-known examples, including CCS [17], πcalculus [12], and Petri nets [16]. Bigraphs consist ess... |

61 | A spatial logic for querying graphs
- Cardelli, Gardner, et al.
(Show Context)
Citation Context ...ng in that it forces names of resources in separated components to be disjoint. As a consequence, term composition is usually partially defined. In static spatial logics (e.g., for, trees [2], graphs =-=[4]-=- or trees with hidden names [5]), the separation/composition does not require any constraint on terms, and names are usually shared between separated parts. Similarly in dynamic spatial logics (for, e... |

59 | 2004): Bigraphs and mobile processes (revised
- Jensen, Milner
(Show Context)
Citation Context ...logic able to express properties of treeshaped structures (and contexts) with pointers, and it is used as an assertion language for Hoare-style program specifications in a tree memory model. Bigraphs =-=[12, 14]-=- are an emerging model for structures in global computing, which can be instantiated to model several well-known examples, including CCS [17], πcalculus [12], and Petri nets [16]. Bigraphs consist ess... |

52 | Deciding Validity in a Spatial Logic for Trees
- Calcagno, Cardelli, et al.
- 2005
(Show Context)
Citation Context ...d it is strong in that it forces names of resources in separated components to be disjoint. As a consequence, term composition is usually partially defined. In static spatial logics (e.g., for, trees =-=[2]-=-, graphs [4] or trees with hidden names [5]), the separation/composition does not require any constraint on terms, and names are usually shared between separated parts. Similarly in dynamic spatial lo... |

43 | U.: Context logic and tree update
- Calcagno, Gardner, et al.
(Show Context)
Citation Context ...etween separated parts. Similarly in dynamic spatial logics (for, e.g., ambients [6] or π-calculus [1]), where the separation is intended only for location in space. Context tree logic, introduced in =-=[3]-=-, integrates the first approach above with a spatial logic for trees. The result is a logic able to express properties of treeshaped structures (and contexts) with pointers, and it is used as an asser... |

36 | Axioms for bigraphical structure
- Milner
(Show Context)
Citation Context ... extending this sharing to all names we can define the parallel composition G | G ′ as a total operation. However, such an operator does not behave “well” with respect to the composition, as shown in =-=[15]-=-. In addition a direct inclusion of a corresponding connective in the logic would impact the satisfaction relation by expanding the finite horizontal decompositions to the boundless possible name-shar... |

33 | Bigraphs for Petri Nets
- Milner
- 2004
(Show Context)
Citation Context ...y model. Bigraphs [12, 14] are an emerging model for structures in global computing, which can be instantiated to model several well-known examples, including CCS [17], πcalculus [12], and Petri nets =-=[16]-=-. Bigraphs consist essentially of two graphs sharing the same nodes. The first graph, the place graph, is tree structured and expresses a hierarchical relationship on nodes (viz. locality in space and... |

32 | Stochastic bigraphs
- Krivine, Milner, et al.
- 2008
(Show Context)
Citation Context ...rogram specifications in a tree memory model. Bigraphs [12, 14] are an emerging model for structures in global computing, which can be instantiated to model several well-known examples, including CCS =-=[17]-=-, πcalculus [12], and Petri nets [16]. Bigraphs consist essentially of two graphs sharing the same nodes. The first graph, the place graph, is tree structured and expresses a hierarchical relationship... |

31 | G.: Manipulating trees with hidden labels
- Cardelli, Fiore, et al.
(Show Context)
Citation Context ...esources in separated components to be disjoint. As a consequence, term composition is usually partially defined. In static spatial logics (e.g., for, trees [2], graphs [4] or trees with hidden names =-=[5]-=-), the separation/composition does not require any constraint on terms, and names are usually shared between separated parts. Similarly in dynamic spatial logics (for, e.g., ambients [6] or π-calculus... |

26 | Transition systems, link graphs and petri nets
- Leifer, Milner
- 2004
(Show Context)
Citation Context ...nal objective is to design a general dynamic logic able to cope uniformly with all the models bigraphs have been proved useful for, as of today these include CCS [17], pi-calculus [12] and Petri-nets =-=[13, 16]-=-. We introduced BiLog, a logic for bigraphs (and more generally for monoidal categories), with two main spatial connectives: composition and tensor product. Our main technical results are the embeddin... |

22 |
Ambient logic
- Cardelli, Gordon
- 2005
(Show Context)
Citation Context ... hidden names [5]), the separation/composition does not require any constraint on terms, and names are usually shared between separated parts. Similarly in dynamic spatial logics (for, e.g., ambients =-=[6]-=- or π-calculus [1]), where the separation is intended only for location in space. Context tree logic, introduced in [3], integrates the first approach above with a spatial logic for trees. The result ... |

8 | An Extensional Spatial Logic for Mobile Processes
- Hirschkoff
- 2004
(Show Context)
Citation Context ...graphs that can compute (react) according to a Bigraphical Reactive System [12]. When the transparency predicate τ enables the inspection of ‘dynamic’ controls, BiLog is ‘intensional’ in the sense of =-=[11]-=-, namely it can observe internal structures. In several cases, notably the bigraphical system describing CCS [17], this can be to the extent that the next step modality can be expressed directly by us... |

7 | Bigraphical logics for XML
- Conforti, Macedonio, et al.
- 2004
(Show Context)
Citation Context ...ications. In particular, the contextual nature of bigraphs is useful to specify reaction rules, but it can also be used as a general mechanism to describe contexts of bigraphical data structures (cf. =-=[8, 10]-=-). As bigraphs are establishing themselves as a truly general (meta)model of global systems, our bigraph logic, BiLog, aims at achieving the same generality as a description language: as bigraphs spec... |

4 | Bigraphs and (Reactive) XML, an XML-centric model of computation - Hildebrandt, Winther - 2005 |