U.Engberg and G. Winskel. Linear logic on Petri nets. LNCS 803, pages 176-- 229, Jun 1993. In A Decade of Concurrency, Reflections and Perspectives, REX School/Symposium. A Syntax for Intuitionistic Temporal Linear Logic Roman capitals A, B, . . . stand for formulas. The connectives of propositional  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a resource conscious logic. Consumption of the data and a dynamic change in process environments can be expressed by linear logic. Some computational models of concurrency are applications of it [1] 7] 17] In particular, the relation between linear logic and Petri nets has been well studied [3], 5] 9] 12] 14] 16] The expressive power is so rich that one can construct a counter machine within the propositional fragment of linear logic. However, it is not enough to treat a dynamic change in process environments with the passage of time. Although [11] is a Graduate School of ....

U.Engberg and G.Winskel, "Linear logic on Petri nets," Lecture Notes in Computer Science, vol.803, pp.176--229, June 1993.

....the dynamic behavior of timed Petri nets by means of the logic. 1 Introduction Linear logic which was introduced by Girard in 1987 [3] has been called a resource conscious logic. The expressive power is evidenced by some very natural encodings of computational models such as Petri nets (PN) [7, 15, 8, 10]. Timed Petri nets (TPN) 2] are place transition nets enhanced with a definite notion of time. In this paper, we focus only on discrete time and describe the relationship between timed Petri nets and logic. Although TPN can be simulated by PN [12] linear logic does not provide natural encodings ....

U.Engberg and G. Winskel. Linear logic on Petri nets. LNCS 803, pages 176-- 229, Jun 1993. In A Decade of Concurrency, Reflections and Perspectives, REX School/Symposium. A Syntax for Intuitionistic Temporal Linear Logic Roman capitals A, B, . . . stand for formulas. The connectives of propositional

....The expressive power is so rich that one can construct a counter machine within the propositional fragment of linear logic. Some computational models of concurrency are applications of LL [26, 2, 20] In particular, the relation between linear logic and Petri nets [11, 36] has been well studied [16, 35, 21, 4, 23]. According to [25] the algebraic point of view of Petri nets seems to be related to the algebraic semantics for linear logic [28, 34] LL has a modal storage operator which means an infinite resource. Using this operator, one can distinguish the treatment of a reusable resource from the ....

U.Engberg and G. Winskel. Linear logic on Petri nets. LNCS 803, pages 176--229, Jun 1993. In A Decade of Concurrency, Reflections and Perspectives, REX School/Symposium.

....a resource conscious logic. Consumption of the data and a dynamic change in process environments can be expressed by linear logic. Some computational models of concurrency are applications of it [1] 7] 17] In particular, the relation between linear logic and Petri nets has been well studied [3], 5] 9] 12] 14] 16] The expressive power is so rich that one can construct a counter machine within the propositional fragment of linear logic. However, it is not enough to treat a dynamic change in process environments with the passage of time. Although [11] is a Graduate School of ....

U.Engberg and G.Winskel, "Linear logic on Petri nets," Lecture Notes in Computer Science, vol.803, pp.176--229, June 1993.

.... = #, if P # [ #] v for all possible valuation v. We say that # entails , written # # , if and only if [ #] v # [ v for all v or, equivalently, # # ] v = tt] v. The structure defined by the spatial operators is not without interest, in particular, #, #, #, 0) is a quantale [5]. 3 Equivalence Between Minimal and Maximal Fixpoint Formulas We define the depth of a process, d(P ) as the depth of its underlying (spatial) tree, that is, the function inductively defined by: d(0) 0, d(n[P ] 1 d(P ) and d(P Q) max d(P ) d(Q) We extend the notion of depth to ....

U. Engberg and G. Winskel. Linear logic on petri nets. Technical Report RS-94-3, BRICS, 1994.

....the MILL cut rule) are interderivable. However, this precise match is obtained by paring down both linear logic and our logic. We can go further and draw a connection with full intuitionistic linear logic, both syntactically and semantically. First, syntactically, intuitionistic linear logic (ILL) [8,11,5] can be embedded in our logic by the mapping: This mapping is such that the rules of ILL can be derived within our logic. In particular, we can derive the strong rules for #that correspond to an interpretation of as a maximal fixpoint, by some non trivial use of our rules. So, 1 , ....

....within our logic. In particular, we can derive the strong rules for #that correspond to an interpretation of as a maximal fixpoint, by some non trivial use of our rules. So, 1 , n LL ILL implies 1 . n LL . The semantic connection is made through quantales [5]. We recall that a (commutative) quantale 4 is a structure S : Set, S 2 Bool, r : 3(S) S, S 2 S, 1 : S such that and r form a complete join semilattice, and 1 form a commutative monoid, and p rQ = r p q q #Q for all p #S and Q S. It is folklore that quantales are ....

Engberg, U.H., Winskel, G.: Linear Logic on Petri Nets. BRICS Report RS-94-3, 1994.

....end, we see the net semantics of SPL as giving a potentially useful, concrete model theory for logics for security protocols. The net runs are histories on which to interpret security properties, perhaps expressed in the style of BAN logic. On another tack, Petri nets form models of linear logic [5], close it seems to the linear logic for security protocols based on multiset rewriting [2] As suggested by an anonymous referee, the expressiveness of SPL could be useful in characterising natural classes of protocols with decidable security properties. Acknowledgements. We are grateful to ....

U. Engberg and G. Winskel. Linear logic on Petri nets. In REX, a decade of concurrency, 1993.

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U.Engberg and G. Winskel. Linear logic on Petri nets. LNCS 803, pages 176-- 229, Jun 1993. In A Decade of Concurrency, Reflections and Perspectives, REX School/Symposium. A Syntax for Intuitionistic Temporal Linear Logic Roman capitals A, B, . . . stand for formulas. The connectives of propositional

No context found.

U.Engberg and G. Winskel. Linear logic on Petri nets. LNCS 803, pages 176--229, Jun 1993. In A Decade of Concurrency, Reflections and Perspectives, REX School/Symposium.

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