Narciso Mart'i-Oliet and Jos'e Meseguer. From Petri nets to linear logic. Technical Report SRI-CSL-89-4R2, SRI International, December 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 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 relationship with Petri nets where there are similar ideas. Places in a Petri net hold to certain ....

....to the token game in Petri nets. Essentially it is shown how a proof of A B in linear logic, where A and B are built from place names just with Omega , corresponds to a play of the token game taking the marking corresponding to A to that corresponding to B. The work of Mart i Oliet and Meseguer [MOM89] extends that of [GG89a] and [Asp87] It is known that certain kinds of linear categories are models for linear logic. The work [MOM89] essentially proceeds by letting Petri nets freely generate a linear category and then interpreting linear logic in that setting. One problem with their approach ....

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Narciso Mart'i-Oliet and Jos'e Meseguer. From Petri Nets to Linear Logic. In Category Theory and Computer Science, Manchester, UK. Springer-Verlag (LNCS 389), 1989.

....logic. 1 Introduction 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 resource conscious logic by Mart i Oliet 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 relationship with Petri nets where there are similar ideas. Places in a Petri net hold to certain ....

....game in Petri nets. Essentially it is shown how a proof of A B in linear logic, where A and B are built from place names just with Omega , corresponds to a play of the token game taking the marking corresponding to A to that corresponding to B. 1 Recent work of Mart i Oliet and Meseguer [MOM89] extends that of [GG89] and [Asp87] It is known that certain kinds of linear categories are models for linear logic. The work [MOM89] essentially proceeds by letting Petri nets freely generate a linear category and then interpreting linear logic in that setting. They restrict attention to ....

[Article contains additional citation context not shown here]

Narciso Mart'i-Oliet and Jos'e Meseguer. From Petri Nets to Linear Logic. In Category Theory and Computer Science, Manchester, UK. Springer-Verlag (LNCS 389), 1989.

....computation and computational reflection. Jos e Meseguer Dr. Meseguer s relevant accomplishments span the following areas: 1. Logic and Formal Methods, including: Formal Models of Security [59, 60] Type Theory [118, 179, 125, 64, 124, 91, 92] Linear, Rewriting, and Equational Logics [94, 93, 95, 119, 98, 96, 64, 124, 123]; Logics and Models of Concurrency [127, 35, 23, 95, 119, 128, 130, 175, 129] Logical Frameworks (General Logics) 117, 120, 24, 96, 97, 126] Formal Methods, Specification and Verification, and Parameterized Programming Methodology [96, 119, 65, 50, 66, 121] 2. Declarative Specification and ....

Narciso Mart'i-Oliet and Jos'e Meseguer. From Petri nets to linear logic. Math. Struct. in Comp. Sci., 1:69--101, 1991.

....Substructural logics and systems specifications There have been many recent efforts to explore the connection between substructural logics and other specification formalisms. Much of this work has been concerned with the principle and correctness of embedding other formalisms, such as Petri Nets [17, 4] and the calculus [3, 10, 18] into Linear Logic. These efforts show the consistency between the different formalisms, but they do not address the issue of the proof environment made available to someone who wants to describe a computational system in one of the formalisms and any pragmatic ....

....in close association with our collaborator, and will benefit from the feedback provided as the implementation is developed and case studies are attempted. 2. 2 Implementation and case studies Marti Oliet and Meseguer propose the use of linear logic axioms as specifications of concurrent systems [17], and indicate the importance of comparing such specifications with more traditional specification techniques. However, there are still few results in this area. In order to perform such a comparison, it is crucial to develop an adequate specification environment linked to a proof tool. The ....

Narciso Marti-Oliet and Jose Meseguer. From Petri nets to linear logic. Mathematical Structures in Computer Science, 1, 1991. 5

....will give extra, quantalic structure. This indeed happens when we take specifications to be sets of processes, and then the logic of specifications is linear. Our work may yield some evidence for the relevance of linear logic to concurrency. Other evidence can be found in work on Petri Nets (e.g. [MOM89]) and testing equivalence [AV90] We introduce our logics in the following overview. Sections 3, 4, and 5 give formal definitions and develop the material further.The reader may wish to consult [DP91, Joh82, Ros90] for information on partial orders, cpos (complete partial orders) complete ....

Narciso Mart'i-Oliet and Jos'e Meseguer. From Petri nets to linear logic. Technical Report SRI-CSL-89-4R2, SRI International, December 1989.

....will give extra, quantalic structure. This indeed happens when we take specifications to be sets of processes, and then the logic of specifications is linear. Our work may yield some evidence for the relevance of linear logic to concurrency. Other evidence can be found in work on Petri Nets (e.g. [22]) and testing equivalence [5] We introduce our logics in Section 2. In Section 3 we develop the intuitionistic logic of safety properties of behaviors, treating also invariance under stuttering. In Section 4 we develop the intuitionistic linear logic of safety properties of processes. As well ....

Narciso Mart'i-Oliet and Jos'e Meseguer. From Petri nets to linear logic. Technical Report SRI-CSL-89-4R2, SRI International, December 1989.

....linear logic with two (equivalent) formalisms: the sequent calculus and the combinators. In terms of category theory, as suggested in their paper, the combinator formulation corresponds to a linear category, i.e. a symmetric monoidal closed category with finite products and coproducts [GL88] [MM89]. One of the well known monoidal closed categories is the one of coherent spaces (with linear maps) Gi87a] In fact, it is in this category that Girard discovered linear logic [Gi87b] based on a crucial observation that the stable function space can be decomposed into more elementary linear ....

Narciso Marti-Oliet, Jose Meseguer, From Petri Nets to Linear Logic, manuscript, (1989).

....semantics to gain a clearer understanding of the denotational meaning of the deduction of the linear logic language. Related work on the use of linear logic for the modelling of computational behaviour includes research by Marti Oliet and Meseguer on the linear logic axiomatization of Petri nets [MOM91] and by Saraswat and Lincoln on linear concurrent constraint programming [SL92] 7 Acknowledgements We would like to thank all the people in the Advanced Languages and Architectures Section in the Department of Computing at Imperial College who provide a stimulating working environment. This ....

Narciso Marti-Oliet and Jose Meseguer. From Petri Nets to Linear Logic. In Category Theory and Computer Science, pages 313--340. Springer, 1991.

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Narciso Mart'i-Oliet and Jos'e Meseguer. From Petri nets to linear logic. Technical Report SRI-CSL-89-4R2, SRI International, December 1989.

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Narciso Mart-Oliet and Jose Meseguer. From Petri Nets to Linear Logic. In Category Theory and Computer Science, Manchester, UK. Springer-Verlag (LNCS 389), 1989.

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MM89 Narciso Marti-Oliet, Jose Meseguer. From Petri Nets to Linear Logic, manuscript, (1989).

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