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This paper is cited in the following contexts:
Petri Nets as Models of Linear Logic - Engberg, Winskel (1990) (30 citations) Self-citation (Logic) (Correct)
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Samson Abramsky and Steve Vickers. Linear Process Logic. Notes by Steve Vickers, 1988.
Linear Logic on Petri Nets - Engberg, Winskel (1994) (8 citations) Self-citation (Logic) (Correct)
....Not everyone is happy with a categorical model as the explanation of a new logic, and in his pioneering paper [Gir87] Girard also gave 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 structures [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 claims for it [Gir87] Linear logic has been described as a ....
....with GOTO statements inserted arbitrarily. 3 Alongside the work on Petri nets and linear logic, came the realisation that models of linear logic had arisen before in the form of quantales. Indeed Girard s phase semantics in [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 ....
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Samson Abramsky and Steve Vickers. Linear Process Logic. Notes by Steve Vickers, 1988.
Petri Nets as Models of Linear Logic - Engberg, Winskel (1990) (30 citations) Self-citation (Logic) (Correct)
....order semantics, of the kind presented here. Alongside the work on Petri nets and linear logic, came the realisation that models of linear logic had arisen before in the form of quantales. Indeed Girard s phase semantics in [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 [Ros] looked at quantales and linear logic more from the perspective of pure mathematics how to represent them and their relationship with other bits ....
....The paper provides evidence that linear intuitionistic logic, with the right notion of satisfaction, can be a reasonably expressive specification logic for parallel processes. It also throws some light on the use of linear classical logic; via a construction, observed by Abramsky and Vickers [AV88], generalising that of Girard s for phase semantics, a quantale can easily be turned into a model for linear classical logic, although unfortunately when taken to nets, the resulting semantics of linear classical logic is often trivial. 2 Linear Intuitionistic Logic In the Gentzen sequent ....
[Article contains additional citation context not shown here]
Samson Abramsky and Steve Vickers. Linear Process Logic. Notes by Steve Vickers, 1988.
Completeness Results for Linear Logic on Petri Nets - Engberg, Winskel (1993) (25 citations) Self-citation (Logic) (Correct)
.... A Omega A (1) B A B 1 B B Omega B B A (2) Given a proposition A, the assertion of A has the possibility of being instantiated by the proposition A, the unit 1 or A Omega A, and thus of arbitrarily many assertions of A. 3 Quantale Interpretation As recognised by several people [AV88, Yet90, Ros90, Sam], quantales 1 provide an algebraic semantics for linear intuitionistic logic. Quantales are to linear intuitionistic logic as complete Heyting algebras are to intuitionistic logic. A quantale is a commutative monoid on a complete join semilattice. Spelled out: Definition 1 A quantale Q is a ....
Samson Abramsky and Steve Vickers. Linear Process Logic. Notes by Steve Vickers, 1988.
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