## Linear logic on Petri nets (1994)

Citations: | 14 - 1 self |

### BibTeX

@TECHREPORT{Engberg94linearlogic,

author = {Uffe H. Engberg and Glynn Winskel},

title = { Linear logic on Petri nets},

institution = {},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

209 | Games and full completeness for multiplicative linear logic - Abramsky, Jagadeesan - 1992 |

163 |
An Algorithm for the General Petri Net Reachability Problem
- Mayr
- 1984
(Show Context)
Citation Context ...ss: j= T A iff ` T A for an arbitrary theory T . Proceed as follows: For a finite net N the set of assertions TN = fM (M 0 j M !M 0 in Ng [ f (M (M 0 ) j M 6! M 0 in Ng is recursively enumerable (see =-=[May84]-=-). Show that with our modified understanding of satisfaction j= N A iff j= TN A: Deduce that there is no effectively given sound and strongly complete proof system. (ii) On the other hand, assuming th... |

141 |
The system F of variable types, fifteen years later. Theoretical Computer Science 45
- Girard
- 1986
(Show Context)
Citation Context ...ard's linear logic arose in part from Girard's insights into particular categorical models for intuitionistic logic. In giving a domain-theoretic semantics to his System F (the polymorphic -calculus) =-=[Gir86]-=-, Girard re-invented the stable domain theory of Berry based on the category dI-domains and stable functions [Ber78], though for rather special domains, the coherence spaces. It turns out that Girard'... |

131 | A game semantics for linear logic - Blass - 1992 |

91 | The linear abstract machine - Lafont - 1988 |

90 | Decision problems for propositional linear logic
- Lincoln, Mitchell, et al.
- 1992
(Show Context)
Citation Context ...n of the notion of a prime theory.] 2 Although we feel sure the logic of section 14 is undecidable i.e. ` A is not decidable for general A, we presently lack a proof (unfortunately, the techniques of =-=[LMSN90]-=- do not work directly because of our primeness axioms). There remain, in addition, the questions of decidability and complexity of weaker fragments of the logic than that of section 14 and their theor... |

67 |
From Petri nets to linear logic
- Martí-Oliet, Meseguer
- 1991
(Show Context)
Citation Context ... might be useful in the theory of parallelism, not least because of Girard's initial claims for it [Gir87]. Linear logic has been described as a "resource conscious" logic by Mart'iOliet and=-= Meseguer [MOM89]-=-; in its proofs occurrences of propositions cannot be used more than once or disappear unless they are explicitly created or used up by the rules of inference. People were not long in spotting a relat... |

43 |
Decidablity questions for Petri nets
- Hack
- 1975
(Show Context)
Citation Context ...50 The property j= N A is undecidable for a finite net N and assertionsA of the of the logic of section 14 (assumed to have infinitely many atomic propositions). Proof From Rabin's work (described in =-=[Hac76]-=-), we know that the question of whether the reachable markings of one finite net are included in the reachable markings of another is undecidable. More precisely, for two finite nets N 1 and N 2 , ove... |

39 | Linear logic and lazy computation - Girard, Lafont - 1987 |

34 | Domain theoretic models of polymorphism
- Coquand, Gunter, et al.
- 1989
(Show Context)
Citation Context ...s construction for modelling polymorphic types can be carried through, with some modifications, in the more standard domain theory based on the category of Scott domains and continuous functions (see =-=[CGW89]-=-). But Girard's use of the category of coherence spaces and stable functions led to a significant discovery, that of classical linear logic. Girard recognised that the category of coherence spaces wit... |

33 | Petri nets as models of linear logic - Engberg, Winskel - 1990 |

27 | Stable models of typed -calculi - Berry - 1978 |

27 | Completeness Results for Linear Logic on Petri Nets (Extended Abstract - Engberg, Winskel |

27 | Graphs and decidable transductions based on edge constraints - Klarlund, Schwartzbach - 1994 |

21 |
Kripke models for linear logic
- Allwein, Dunn
- 1993
(Show Context)
Citation Context ...a "phase--space" semantics for linear logic. There have since been investigations of several other kinds of structures as models of linear logic, quantales (e.g.[AV88]), generalised Kripke s=-=tructures [AD93]-=-, and Petri nets---the main topic here. Girard's linear logic has sparked off a great deal of interest in how it might be useful in the theory of parallelism, not least because of Girard's initial cla... |

21 |
A logic for concurrency
- Asperti
- 1987
(Show Context)
Citation Context ...tions occur, multiplicities of places are consumed and produced in accord with a dynamic behaviour of nets, formalised in the so-called "token game". Independently, Gunter and Gehlot [GG89a]=-=, Asperti [Asp87]-=- and Brown [Bro89] showed that places are like atomic propositions in linear logic and transitions like proof rules. In [GG89a] and [Asp87], the fine grain of linear logic proofs for the \Omega -fragm... |

18 |
Nets: An Introduction, volume 4
- Petri
- 1985
(Show Context)
Citation Context ...ber of tokens residing on a place expresses the multiplicity to which it holds according to the marking. The tokens are consumed and produced as transitions occur. A basic reference for Petri nets is =-=[Rei85]-=-. Since we are dealing with place/transition nets without capacities we have the following proposition which is crucial for the net semantics of linear logic in the sequel. Proposition 5 For any M;M 0... |

17 |
Relating Petri Nets to Formulae of Linear Logic
- Brown
- 1989
(Show Context)
Citation Context ...plicities of places are consumed and produced in accord with a dynamic behaviour of nets, formalised in the so-called "token game". Independently, Gunter and Gehlot [GG89a], Asperti [Asp87] =-=and Brown [Bro89]-=- showed that places are like atomic propositions in linear logic and transitions like proof rules. In [GG89a] and [Asp87], the fine grain of linear logic proofs for the \Omega -fragment of linear logi... |

16 | Stable models of typed λ-calculi - Berry - 1978 |

6 | Complexity of Nondeterministic Functions - Andreev - 1994 |

4 |
and Vijay Gehlot. Nets as tensor theories
- Gunter
- 1989
(Show Context)
Citation Context ...(filling out that of [EW90, EW93]) contrasts with other approaches to linear logic on Petri nets in that they either apply only to much smaller fragments of the logic such as the\Omega -fragment (cf. =-=[GG89b]-=-), or use the transitions of a Petri net to freely generate a linear-logic theory (cf. [MOM91]), in which case the logic becomes rather inexpressive, and in particular cannot capture negative 4 proper... |

2 |
and Vijay Gehlot. A Proof-Theoretic Operational Semantics for True Concurrency
- Gunter
- 1989
(Show Context)
Citation Context ...arking; as transitions occur, multiplicities of places are consumed and produced in accord with a dynamic behaviour of nets, formalised in the so-called "token game". Independently, Gunter a=-=nd Gehlot [GG89a]-=-, Asperti [Asp87] and Brown [Bro89] showed that places are like atomic propositions in linear logic and transitions like proof rules. In [GG89a] and [Asp87], the fine grain of linear logic proofs for ... |

2 |
From Petri Nets to Linear Logic: a Survey
- Mart'i-Oliet, Meseguer
- 1991
(Show Context)
Citation Context ...ts in that they either apply only to much smaller fragments of the logic such as the\Omega -fragment (cf. [GG89b]), or use the transitions of a Petri net to freely generate a linear-logic theory (cf. =-=[MOM91]-=-), in which case the logic becomes rather inexpressive, and in particular cannot capture negative 4 properties, or they don't address completeness at all. 2 Intuitionistic Linear Logic In the Gentzen ... |

2 |
A Note on Girard Quantales
- Rosenthal
(Show Context)
Citation Context ...ogic uses free quantales. Abramsky and Vickers [AV88] approached quantales from a computer science viewpoint, the hope being that it would lead to a "linear process logic". Yetter [Yet] and =-=Rosenthal [Ros89]-=- looked at quantales and linear logic more from the perspective of pure mathematics---how to represent them and their relationship with other bits of mathematics. We point out a straightforward way in... |

2 |
Quantales and Non-Commutative Linear Logic. (preprint
- Yetter
(Show Context)
Citation Context ...[Gir87] for linear logic uses free quantales. Abramsky and Vickers [AV88] approached quantales from a computer science viewpoint, the hope being that it would lead to a "linear process logic"=-=;. Yetter [Yet]-=- and Rosenthal [Ros89] looked at quantales and linear logic more from the perspective of pure mathematics---how to represent them and their relationship with other bits of mathematics. We point out a ... |

2 | Martí-Oliet and José Meseguer. From Petri Nets to Linear Logic - Narciso - 1989 |

1 |
An existence predicate for a linear logic of Petri net
- Cattani
(Show Context)
Citation Context ...ation with the present semantics is that all atoms must name places, or more precisely their downwards closure with respect to reachability, possibly in a many-one way. Gian Luca Cattani has shown in =-=[Cat]-=- that the semantics can be relaxed to allow atoms to denote false at the slight cost of adding existence conditions to the logic and changing the substitution rule. Another extension would be to add t... |

1 | A Logic for Concurrency. manuscript - Asperti - 1987 |

1 | Manuscript reported to us by Per - et - 1989 |