## A Spatial Logic for Concurrency (Part II) (1998)

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Venue: | IN CONCUR2002: CONCURRENCY THEORY (13TH INTERNATIONAL CONFERENCE), LECTURE NOTES IN COMPUTER SCIENCE |

Citations: | 55 - 7 self |

### BibTeX

@INPROCEEDINGS{Caires98aspatial,

author = {Luís Caires and Luca Cardelli},

title = {A Spatial Logic for Concurrency (Part II)},

booktitle = {IN CONCUR2002: CONCURRENCY THEORY (13TH INTERNATIONAL CONFERENCE), LECTURE NOTES IN COMPUTER SCIENCE},

year = {1998},

pages = {42--56},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

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### Abstract

### Citations

713 | Separation logic: A logic for shared mutable data structures
- Reynolds
- 2002
(Show Context)
Citation Context ...equivalence [16]. The work of Gabbay and Pitts on the freshness quantifier [10] has become central to our logic. The work of O’Hearn and Pym on Bunched Logics [12] and of Reynolds on Separation Logic =-=[15]-=- is closely related to ours, at least in intent. The style in which the logic is formalized is an extension of work by Alex Simpson [17], and is also related, at least superficially, to labeled deduct... |

495 | R.: Algebraic laws for nondeterminism and concurrency
- Hennessy, Milner
- 1985
(Show Context)
Citation Context ...f such a logic as a proper sequent calculus. Moreover, we now target the logic towards a more standard �-calculus. The first main difference between our logic and standard logics of concurrency (e.g. =-=[11]-=-) is the presence in our case of a tensor operator that corresponds to process composition. Usually, those other logics require formulas to denote processes up to bisimulation, which is difficult to r... |

191 | The logic of bunched implications
- O’Hearn, Pym
- 1999
(Show Context)
Citation Context ...the logic is then essentially structural equivalence [16]. The work of Gabbay and Pitts on the freshness quantifier [10] has become central to our logic. The work of O’Hearn and Pym on Bunched Logics =-=[12]-=- and of Reynolds on Separation Logic [15] is closely related to ours, at least in intent. The style in which the logic is formalized is an extension of work by Alex Simpson [17], and is also related, ... |

165 | Nominal logic, a first order theory of names and binding
- Pitts
(Show Context)
Citation Context ...ularize and generalize the logics introduced in [1, 7, 8], and we prove a cut-elimination result for the first-order fragment, including cut-elimination for a fresh name quantifier (cf. Nominal Logic =-=[13]-=-). A formula in our logic describes a property of a particular part of a concurrent system (a world) at a particular time; therefore it is modal in space as well as in time. In our sequents, formulas ... |

162 | Anytime, anywhere. Modal logics for mobile ambients
- Cardelli, Gordon
- 2000
(Show Context)
Citation Context ... intended model, which is used here to establish the soundness of the logical rules. The central focus of this Part II, however, is proof theory. We regularize and generalize the logics introduced in =-=[1, 7, 8]-=-, and we prove a cut-elimination result for the first-order fragment, including cut-elimination for a fresh name quantifier (cf. Nominal Logic [13]). A formula in our logic describes a property of a p... |

145 | A new approach to abstract syntax involving binders
- Gabbay, Pitts
- 1999
(Show Context)
Citation Context ... 1], and later independently in [8]. Our current understanding is that it is best to decompose such a hiding quantifier into two operators: a modal version of the fresh quantifier of Gabbay and Pitts =-=[10]-=-, and a logical operator, called revelation [8], that relates to name hiding in strong analogy to the way tensor relates to process composition. A simple combination of fresh quantification and revela... |

136 | A spatial logic for concurrency (part I
- Caires, Cardelli
- 2001
(Show Context)
Citation Context ...ulus). Our formulas denote collections of processes subject to certain closure conditions, with some logical operators mapping directly to process composition and name hiding. In Part I of this paper =-=[2, 4]-=- we study this intended model, which is used here to establish the soundness of the logical rules. The central focus of this Part II, however, is proof theory. We regularize and generalize the logics ... |

124 | A logic for parametric polymorphism
- Plotkin, Abadi
- 1993
(Show Context)
Citation Context ... in Part I. In this paper we go one step further and introduce second-order quantification in the logic, from which we can define least and greatest fixpoints of formulas, almost along standard lines =-=[14]-=-. Structurally, our logic consists of a collection of left-right rules for logical operators, including essentially the standard rules of classical sequent calculus, plus the ones for temporal and spa... |

100 | The Proof Theory and Semantics of Intuitionistic Modal Logic
- Simpson
- 1994
(Show Context)
Citation Context ... of a particular part of a concurrent system (a world) at a particular time; therefore it is modal in space as well as in time. In our sequents, formulas are indexed by the worlds they predicate over =-=[17]-=-, so a sequent can talk about many distinct worlds at once. Each sequent incorporates also a finite set of constraints over the worlds, including process reduction and congruence constraints. In gener... |

52 | Deciding Validity in a Spatial Logic for Trees
- Calcagno, Cardelli, et al.
- 2005
(Show Context)
Citation Context ...y Alex Simpson [17], and is also related, at least superficially, to labeled deductive systems [18]. A decidable and complete propositional fragments of a related logic has been recently investigated =-=[6]-=-. In Section 2 we introduce the algebra of constraints. In Section 3 we introduce our sequent calculus, which can be shown sound by an interpretation in the model of Part I. In Section 4 we investigat... |

46 | Logical properties of name restriction
- Cardelli, Gordon
- 2001
(Show Context)
Citation Context ... intended model, which is used here to establish the soundness of the logical rules. The central focus of this Part II, however, is proof theory. We regularize and generalize the logics introduced in =-=[1, 7, 8]-=-, and we prove a cut-elimination result for the first-order fragment, including cut-elimination for a fresh name quantifier (cf. Nominal Logic [13]). A formula in our logic describes a property of a p... |

42 | Extensionality and intensionality of the ambient logics, in
- Sangiorgi
- 2000
(Show Context)
Citation Context ...uctural equivalence, so that a tensor operator makes easy sense. Sangiorgi has shown, for a closely related logic, that the equivalence induced by the logic is then essentially structural equivalence =-=[16]-=-. The work of Gabbay and Pitts on the freshness quantifier [10] has become central to our logic. The work of O’Hearn and Pym on Bunched Logics [12] and of Reynolds on Separation Logic [15] is closely ... |

37 |
Labelled Non-Classical Logics
- Viganò
- 2000
(Show Context)
Citation Context ...Each sequent incorporates also a finite set of constraints over the worlds, including process reduction and congruence constraints. In general, the constraint structure can be fashioned as an algebra =-=[18]-=-; which in our case is a relatively complex process algebra. The fragment of our logic that deals with process composition is relatively straightforward: composition shows up in the logic as a tensor,... |

18 | A Model for Declarative Programming and Specification with Concurrency and Mobility
- Caires
- 1999
(Show Context)
Citation Context ... intended model, which is used here to establish the soundness of the logical rules. The central focus of this Part II, however, is proof theory. We regularize and generalize the logics introduced in =-=[1, 7, 8]-=-, and we prove a cut-elimination result for the first-order fragment, including cut-elimination for a fresh name quantifier (cf. Nominal Logic [13]). A formula in our logic describes a property of a p... |

16 |
Relevance logic and concurrent composition
- Dam
- 1988
(Show Context)
Citation Context ...to denote processes up to bisimulation, which is difficult to reconcile with a tensor operator that can make distinctions between bisimilar processes (however, such an operator was anticipated by Dam =-=[9]-=-). In our case, we only require formulas to denote processes up to structural equivalence, so that a tensor operator makes easy sense. Sangiorgi has shown, for a closely related logic, that the equiva... |

10 |
Verifiable and executable specifications of concurrent objects in Lπ
- Caires, Monteiro
- 1998
(Show Context)
Citation Context ...r” that binds a private name in a formula; such a formula could then describe the use of that private name in the process. The study of such a quantifier, from a logical point of view, was started in =-=[5, 1]-=-, and later independently in [8]. Our current understanding is that it is best to decompose such a hiding quantifier into two operators: a modal version of the fresh quantifier of Gabbay and Pitts [10... |