## A Logical and Computational Theory of Located Resource (2008)

Citations: | 13 - 9 self |

### BibTeX

@MISC{Collinson08alogical,

author = {Matthew Collinson and Brian Monahan and David Pym},

title = {A Logical and Computational Theory of Located Resource},

year = {2008}

}

### OpenURL

### Abstract

Experience of practical systems modelling suggests that the key conceptual components of a model of a system are processes, resources, locations, and environment. In recent work, we have given a process-theoretic account of this view in which resources as well as processes are first-class citizens. This process calculus, SCRP, captures the structural aspects of the semantics of the Demos2k modelling tool. Demos2k represents environment stochastically using a wide range of probability distributions and queue-like data structures. Associated with SCRP is a (bunched) modal logic, MBI, which combines the usual additive connectives of Hennessy-Milner logic with their multiplicative counterparts. In this paper, we complete our conceptual framework by adding to SCRP and MBI an account of a notion of location that is simple, yet sufficiently expressive to capture naturally a wide range of forms of location, both spatial and logical. We also provide a description of an extension of the Demos2k tool to incorporate this notion of location. 1

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Citation Context ...e of resource which is distributed around a space of locations. The techniques we will bring to bear will be those of logic and theoretical computer science, particularly synchronous process calculus =-=[27, 28, 29]-=-. Process calculi are formal systems that allow for the compositional construction of discrete dynamical systems. As such they may be fruitfully regarded as idealized languages for modelling and simul... |

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Citation Context ...hilst the process component is used, primarily, to represent active entities (agents). The notion of resource (e.g., space, memory, money) taken corresponds to the resource semantics of bunched logic =-=[34, 37, 38, 39]-=-, based on (ordered, partial, commutative) monoids (e.g., the non-negative integers with zero, addition, and less-than-or-equals), which captures the following basic properties of resources: • Each ty... |

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Citation Context ...hilst the process component is used, primarily, to represent active entities (agents). The notion of resource (e.g., space, memory, money) taken corresponds to the resource semantics of bunched logic =-=[34, 37, 38, 39]-=-, based on (ordered, partial, commutative) monoids (e.g., the non-negative integers with zero, addition, and less-than-or-equals), which captures the following basic properties of resources: • Each ty... |

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Citation Context |

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Citation Context ...bscure the evolution of those features (location and resource) and add computational burden. Pym and Tofts, and also Collinson, have initiated a line of research which explictly takes a contrary view =-=[16, 17, 40, 41]-=-. In the SCRP family of calculi, system states carry a resource ∗ matthew.collinson@hp.com † brian.monahan@hp.com ‡ david.pym@hp.com § All authors: HP Labs, Stoke Gifford, Bristol BS34 8QZ, England, U... |

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Citation Context ...ted resources. This tool is an extension of the existing Demos2k (D2k) 3tool. D2k has been used extensively in large-scale commercial projects undertaken by, and related to, HP’s services businesses =-=[46, 51, 3, 4]-=-. Our intention is that LD2k should bear the same relation to LSCRP as D2k does to SCRP. In particular, LSCRP should be able to serve as a theoretical foundation for LD2k. There are a number of altern... |

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Citation Context ...bscure the evolution of those features (location and resource) and add computational burden. Pym and Tofts, and also Collinson, have initiated a line of research which explictly takes a contrary view =-=[16, 17, 40, 41]-=-. In the SCRP family of calculi, system states carry a resource ∗ matthew.collinson@hp.com † brian.monahan@hp.com ‡ david.pym@hp.com § All authors: HP Labs, Stoke Gifford, Bristol BS34 8QZ, England, U... |

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Citation Context ...on graph and resource distribution. Simple modal assertions describe the one-step evolution of the system as follows: L1, R1, E1 � 〈move(r, l, m, 1)〉φ (0,1) ∧ [move(r, l, m, 1)]φ (0,1) ∧ 〈1〉φ (1,0) ∧ =-=[1]-=-φ (1,0) . 30If there is any other process G such that G has a tick action, then and so L1, R1, E1 × G � 〈move(r, l, m, 1)〉φ (0,1) L1,eR, E1 � (φ (1,0) ∧ 〈1〉⊤) −∗ 〈move(r, l, m, 1)〉φ (0,1) (1) holds. ... |

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Citation Context ...xecution trace (too long to be included in this paper) is presented in [14]. There are some very minor differences in the syntax of the code presented in there (the model is executed as an OCAML term =-=[32, 42]-=-) but for our purposes this distinction is superficial. (∗ Example LD2k model : Secure information flow control ∗) (∗ constant declarations : no distributions yet ∗) 20const ferryin = 2; const ferryd... |

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Citation Context ... (and possibly atomic links) in atomic formulae and quantification over such variables. Further examples of the use of ∗ and −∗ in reasoning about resource and process (but not location) are given in =-=[40, 41]-=-. More complex properties of systems often require enrichments of the logical language presented here, for example ‘always’ or ‘eventually’ modalities. 7 Discussion We have produced a theoretical fram... |

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Citation Context ...ractical systems modelling situations. The kinds of examples we consider are often quite detailed. In order to be able to tackle these examples efficiently, we have constructed Located Demos2k (LD2k) =-=[12, 13, 14]-=-, a prototype tool for modelling with distributed resources. This tool is an extension of the existing Demos2k (D2k) 3tool. D2k has been used extensively in large-scale commercial projects undertaken... |

5 |
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(Show Context)
Citation Context ... lie at the nodes of certain trees, and mobility corresponds to the ability of process terms to dynamically reconfigure such trees. An even more sophisticated system is the bigraph approach of Milner =-=[26, 31]-=-. As the name (perhaps) suggests, a bigraph is a mathematical structure that combines two types of structure. It has both a graph signifying connectivity and a graph signifying the sublocation relatio... |

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Citation Context ...ted resources. This tool is an extension of the existing Demos2k (D2k) 3tool. D2k has been used extensively in large-scale commercial projects undertaken by, and related to, HP’s services businesses =-=[46, 51, 3, 4]-=-. Our intention is that LD2k should bear the same relation to LSCRP as D2k does to SCRP. In particular, LSCRP should be able to serve as a theoretical foundation for LD2k. There are a number of altern... |

3 |
Located Demos2k: A tool for executing processes relative to distributed resources
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(Show Context)
Citation Context ...ractical systems modelling situations. The kinds of examples we consider are often quite detailed. In order to be able to tackle these examples efficiently, we have constructed Located Demos2k (LD2k) =-=[12, 13, 14]-=-, a prototype tool for modelling with distributed resources. This tool is an extension of the existing Demos2k (D2k) 3tool. D2k has been used extensively in large-scale commercial projects undertaken... |

3 |
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(Show Context)
Citation Context ...ted resources. This tool is an extension of the existing Demos2k (D2k) 3tool. D2k has been used extensively in large-scale commercial projects undertaken by, and related to, HP’s services businesses =-=[46, 51, 3, 4]-=-. Our intention is that LD2k should bear the same relation to LSCRP as D2k does to SCRP. In particular, LSCRP should be able to serve as a theoretical foundation for LD2k. There are a number of altern... |