## Anytime, anywhere: modal logics for mobile ambients (2000)

### Cached

### Download Links

- [lucacardelli.name]
- [research.microsoft.com]
- [research.microsoft.com]
- DBLP

### Other Repositories/Bibliography

Venue: | In POPL ’00: Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages |

Citations: | 169 - 14 self |

### BibTeX

@INPROCEEDINGS{Cardelli00anytime,anywhere:,

author = {Luca Cardelli and Andrew D. Gordon},

title = {Anytime, anywhere: modal logics for mobile ambients},

booktitle = {In POPL ’00: Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages},

year = {2000},

pages = {365--377},

publisher = {ACM}

}

### Years of Citing Articles

### OpenURL

### Abstract

The Ambient Calculus is a process calculus where processes may reside within a hierarchy of locations and modify it. The purpose of the calculus is to study mobility, which is seen as the change of spatial configurations over time. In order to describe properties of mobile computations we devise a modal logic that can talk about space as well as time, and that has the Ambient Calculus as a model. 1

### Citations

845 | Mobile ambients
- Cardelli, Gordon
- 1998
(Show Context)
Citation Context ...es of mobile computations we devise a modal logic that can talk about space as well as time, and that has the Ambient Calculus as a model. 1 Introduction In the course of our ongoing work on mobility =-=[3,4,5,12]-=-, we have often struggled to express precisely certain properties of mobile computations. Informally, these are properties such as “the agent has gone away”, “eventually the agent crosses the firewall... |

592 |
Untersuchungen über das logische Schließen. Mathematische Zeitschrift, 39:176–210 and 405–431
- Gentzen
- 1934
(Show Context)
Citation Context ... bunched logic [18]. We discuss this further in Section 6. Noticeably, we abandon Gentzen’s distinction between structural rules and other logical rules, which has been a staple of formal logic since =-=[11]-=-. We do not see this as a fundamental or irrevocable step. Not all logics fit easily into Gentzen’s initial approach, and many alternative sequent structures have been studied [7]. Therefore, there ma... |

512 | Algebraic laws for nondeterminism and concurrency
- Hennessy, Milner
- 1985
(Show Context)
Citation Context ...nal flavor that distinguishes our logic from other modal logics for concurrency. Previous work in the area concentrates on properties that are invariant up to strong equivalences such as bisimulation =-=[15,6]-=-, while our properties are invariant only up to simple spatial rearrangements. Some of our techniques can be usefully applied to other process calculi, even ones that do not have locations, such as CC... |

374 |
Proofs and Types
- Girard, Lafont, et al.
- 1989
(Show Context)
Citation Context ...del, and into tables of Corollaries, which are derived purely logically from the inference rules. 4.2.1 Propositions The following is a non-standard presentation of the propositional sequent calculus =-=[14]-=-, based on our single-assumption single-conclusion sequents. In this presentation, the rules of propositional logic become very symmetrical, and many proofs become more regular, having to consider onl... |

162 | Types for mobile ambients
- Cardelli, Gordon
- 1999
(Show Context)
Citation Context ...es of mobile computations we devise a modal logic that can talk about space as well as time, and that has the Ambient Calculus as a model. 1 Introduction In the course of our ongoing work on mobility =-=[3,4,5,12]-=-, we have often struggled to express precisely certain properties of mobile computations. Informally, these are properties such as “the agent has gone away”, “eventually the agent crosses the firewall... |

98 | Seal: A framework for secure mobile computations
- Vitek, Castagna
- 1999
(Show Context)
Citation Context ...pond to names of sublocations, and subtrees correspond to sublocations. Such a representation of locations is shared by the Ambient Calculus [3], the Distributed Join Calculus [10], the Seal Calculus =-=[20]-=-, and trivially by the many distributed process calculi with a flat location structure (e.g.: [2]). The following edge-labeled tree represents two contiguous locations, a and b, such that b has no sub... |

93 |
The linear abstract machine
- Lafont
- 1988
(Show Context)
Citation Context ...linear logic and our logic. We can go further and draw a connection with full intuitionistic linear logic, both syntactically and semantically. First, syntactically, intuitionistic linear logic (ILL) =-=[13,16,8]-=- can be embedded in our logic by the mapping: $ ⊕ % $ $ ∨ % $ & % $ $ ∧ % $ ⊗ % $ $ | % $ xyµ % $ $ © % !$ $ 0 ∧ (0 ⇒ $)¬F 1ILL $ 0 ŒILL $ F �ILL $ T $ F 0ILL This mapping is such that the rules of IL... |

59 | Localities and failures
- Amadio, Prasad
- 1994
(Show Context)
Citation Context ...ocations is shared by the Ambient Calculus [3], the Distributed Join Calculus [10], the Seal Calculus [20], and trivially by the many distributed process calculi with a flat location structure (e.g.: =-=[2]-=-). The following edge-labeled tree represents two contiguous locations, a and b, such that b has no sublocations, and a has a sublocation called p. The diagram on the right gives a more intuitive but ... |

58 | Equational Properties for Mobile Ambients
- Cardelli, Gordon
- 1999
(Show Context)
Citation Context ...es of mobile computations we devise a modal logic that can talk about space as well as time, and that has the Ambient Calculus as a model. 1 Introduction In the course of our ongoing work on mobility =-=[3,4,5,12]-=-, we have often struggled to express precisely certain properties of mobile computations. Informally, these are properties such as “the agent has gone away”, “eventually the agent crosses the firewall... |

39 |
Linear logic and lazy computation
- Girard, Lafont
- 1986
(Show Context)
Citation Context ...linear logic and our logic. We can go further and draw a connection with full intuitionistic linear logic, both syntactically and semantically. First, syntactically, intuitionistic linear logic (ILL) =-=[13,16,8]-=- can be embedded in our logic by the mapping: $ ⊕ % $ $ ∨ % $ & % $ $ ∧ % $ ⊗ % $ $ | % $ xyµ % $ $ © % !$ $ 0 ∧ (0 ⇒ $)¬F 1ILL $ 0 ŒILL $ F �ILL $ T $ F 0ILL This mapping is such that the rules of IL... |

37 | A logical view of composition
- Abadi, Plotkin
- 1993
(Show Context)
Citation Context ...ies the formula —$ if $ holds at some sublocation P’ within P, where “sublocation” is defined by P‹ * P’. The last two connectives, @ and ©, can be used to express assumption/guarantee specifications =-=[1]-=-; they were inspired by the wish to express security properties. A reading of P Ÿ $@n is that P (together with its context) manages to satisfy $ even when placed into a location called n. A reading of... |

33 |
Semantics for relevant logics
- Urquhart
- 1972
(Show Context)
Citation Context ...pare our logic with well known substructural logics. 6.1 Relevant Logic The shape of our definition of the satisfaction relation turns out to be very similar to Urquhart’s semantics of relevant logic =-=[19]-=-. (Thanks to Peter O’Hearn and David Pym for pointing this out.) In particular $_% is similar to intensional conjunction, and $©% is similar to relevant implication in that semantics. The main differe... |

30 |
Flow graphs and flow algebras
- Milner
- 1979
(Show Context)
Citation Context ...following table summarizes the syntax of processes. We have separated the process constructs into spatial and temporal; this is similar to the distinction between static and dynamic constructs in CCS =-=[17]-=-. This paper focuses on the spatial constructs; the temporal constructs and the dynamic behavior are necessary but secondary for our current purposes. Processes P,Q,R ::= 0 P | Q !P M[P] M.P (n).P jMk... |

29 |
A historical introduction to substructural logics, Substructural Logics
- Došen
- 1993
(Show Context)
Citation Context ... formal logic since [11]. We do not see this as a fundamental or irrevocable step. Not all logics fit easily into Gentzen’s initial approach, and many alternative sequent structures have been studied =-=[7]-=-. Therefore, there may be formulations of our logic which identify a set of structural rules, perhaps along the lines of [18]. At the current stage in the development of our logic, however, it is uncl... |

16 |
Relevance logic and concurrent composition
- Dam
- 1988
(Show Context)
Citation Context ...nal flavor that distinguishes our logic from other modal logics for concurrency. Previous work in the area concentrates on properties that are invariant up to strong equivalences such as bisimulation =-=[15,6]-=-, while our properties are invariant only up to simple spatial rearrangements. Some of our techniques can be usefully applied to other process calculi, even ones that do not have locations, such as CC... |

13 | Linear logic on Petri nets
- Engberg, Winskel
- 1994
(Show Context)
Citation Context ...linear logic and our logic. We can go further and draw a connection with full intuitionistic linear logic, both syntactically and semantically. First, syntactically, intuitionistic linear logic (ILL) =-=[13,16,8]-=- can be embedded in our logic by the mapping: $ ⊕ % $ $ ∨ % $ & % $ $ ∧ % $ ⊗ % $ $ | % $ xyµ % $ $ © % !$ $ 0 ∧ (0 ⇒ $)¬F 1ILL $ 0 ŒILL $ F �ILL $ T $ F 0ILL This mapping is such that the rules of IL... |

5 |
D.: The Logic of Bunched Implications. Bulletin of Symbolic Logic
- O’Hearn, Pym
- 1999
(Show Context)
Citation Context ...f L} as a structural operator, all the rules of intuitionistic linear logic can be derived. Finally, by taking nestings of ∧ and | on the left of L} as structural “bunches”, we obtain a bunched logic =-=[18]-=-. We discuss this further in Section 6. Noticeably, we abandon Gentzen’s distinction between structural rules and other logical rules, which has been a staple of formal logic since [11]. We do not see... |

5 |
A multiset semantics for the π-calculus with replication
- Engelfriet
- 1996
(Show Context)
Citation Context ...o say that this completeness result motivates the choice of axioms for structural congruence, and particularly the axioms for replication (which are the same as in Engelfriet’s work on the π-calculus =-=[9]-=-). Reduction n[in m. P | Q] | m[R] xyyz m[n[P | Q] | R] (Red In) m[n[out m. P | Q] | R] xyyz n[P | Q] | m[R] (Red Out) open n. P | n[Q] xyyz P | Q (Red Open) (n).P | jMk xyyz P{n←M} (Red Comm) P xyyz ... |

1 | A Multiset Semantics for the pp-calculus with Replication - Engelfriet - 1996 |

1 | The Linear Abstract Machine. TCS - Lafont - 1988 |