Citations: From Petri nets to linear logic through categories: A survey

38 citations found. Retrieving documents...

N. Mart-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. Journal on Foundations of Computer Science, 2(4):297-399, December 1991.

Home/Search Document Not in Database Summary Related Articles Check

This paper is cited in the following contexts:

First 50 documents

A concurrent logical framework I: Judgments and.. - Watkins, Cervesato.. (2003) (2 citations) (Correct)

.... [Pfe99] Further examples of CLF representations, including a full development of the Petri net example, are in the technical report by Cervesato et al. CPWW02] The idea of representing Petri nets by linear hypothetical judgments has a long history, going back to Mart Oliet and Meseguer [MOM91]. Monadic encapsulation in the context of functional programming and type theory begins with Moggi s monadic metalanguage [Mog89, Mog91] Prawitz describes a proof theory for modal logics [Pra65] from which Moggi s presentation of the monadic metalanguage inherits. Pfenning and Davies [PD01] ....

N. Mart-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. Journal on Foundations of Computer Science, 2(4):297-399, December 1991.

A Concurrent Logical Framework: the - Propositional Fragment Kevin (Correct)

....in Section 2.2. The typing rules for the canonical variant of LLF 0 are shown in Figure 1. An example. A Petri net serves as a running example of the various encoding techniques used in these frameworks. The representation of Petri nets in linear logic goes back to Mart Oliet and Meseguer [MOM91], but has been treated several times in the literature. Familiarity with Petri nets is assumed, and their encoding is : A N ( B ; x: N ( A B ; u : A; N ( B ; u: N ( A B ; N1 ( A ; N2 ( B ; hN1 ; N2 i ( A B I ; hi ( I ; R ) a ; R ( a ....

....is captured by cut elimination (normalization) steps over linear logic derivations. A second direction, which may be identi ed with the slogan proofs as traces (and formulas as processes) models dynamic process behaviors as proof search, generally in the style of (linear) logic programming [MOM91,And92,Mil92,KY93,Chi95,Cer95]. CLF follows this second path, stressing a one to one correspondence between CLF proof terms and process executions (traces) CPWW02] CLF di ers from most of these proposals in two respects: rst, it is a fully edged logical framework, which means that it expresses not only the constructs of ....

N. Mart-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. Journal on Foundations of Computer Science, 2(4):297{ 399, December 1991.

Unknown - Sequent Calculus In (Correct)

....and derivation of ; A = C ; C. Proof: By simultaneous induction on the structure of the derivations of ; A and ; A #. 2 3.2 Another Example: Petri Nets In this section we show 1 how to represent Petri nets in linear logic. This example is due to Mart Oliet and Meseguer [MOM91], but has been treated several times in the literature. 3.3 Deductions with Lemmas One common way to nd or formulate a proof is to introduce a lemma. In the sequent calculus, the introduction and use of a lemma during proof search is modelled by the rules of cut, Cut for lemmas used as linear ....

N. Mart-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. Journal on Foundations of Computer Science, 2(4):297-399, December 1991.

Unknown - Sequent Calculus In (Correct)

....C and derivation of ; A = C ; C. Proof: By simultaneous induction on the structure of the derivations of ; A and ; A #. 2 3.2 Another Example: Petri Nets In this section we show how to represent Petri nets in linear logic. This example is due to Mart Oliet and Meseguer [MOM91], but has been treated several times in the literature. A Petri net is de ned by a collection of places, transitions, arcs, and tokens. Every transition has input arcs and output arcs that connect it to places. The system evolves by changing the tokens in various places according to the ....

N. Mart-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. Journal on Foundations of Computer Science, 2(4):297-399, December 1991.

Branching processes of Petri nets in the context of the "nets in.. - Köhler (2000) (Correct)

....theory the function f could be regarded as the forgetful functor to the functor NDP [ which constructs the DP net. The functor f reduces the process of the net N to the net itself (for a description of the category theory and its use in the context of the Petri nets s.a. BW90] ML71] and [MOM91]) The function f can be extended on markings P x i in a natural way: f(m) f( X x i ) X f(x i ) Theorem 1 From the construction of NDP [N ] it follows, that: t x i = t x i = X x i x FDP y = f(x) F f(y) Theorem 2 Furthermore, we have: f(t x i ) f( t x i ) f( ....

Narciso Mart-Oliet and Jos Meseguer. From petri nets to linear logic through categories: a survey. Foundations of computer science, 2:297399, 1991.

Petri Net Semantics of Bunched Implications - O'Hearn, Yang (Correct)

....Winskel, and we argue that it provides a more natural logic for the net semantics. We then brie y consider a more expressive logic based on an extension of BI with classical and modal features. 1 Introduction A number of authors have explored the connection between Petri nets and linear logic [5, 8, 19, 9, 24, 25]. The basic idea is to encode markings as tensor products a 1 an of atomic formulae, and transitions as judgements M N with markings in antecedent and consequent positions. Given a judgement of this form as an axiom, for each transition in a net, one obtains that M N is derivable from ....

....as in branching time temporal logics, Hennessy Milner logic or temporal logic based on partial order semantics [15, 33, 4, 30, 31] but in a way compatible with multiplicative conjunction. There have, to date, been a number of suggestive uses of substructural logics in concurrency (e.g. [11, 3, 2, 22, 8, 19, 9, 24, 25]) While there has not yet been a de nitive or completely convincing account, the idea of using multiplicative conjunction to describe spatial distribution of resources or processes remains appealing. In this connection it is worth stressing, in conclusion, that there appears to be no compelling ....

N. Mart-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. Journal on Foundations of Computer Science, 2(4):297-399, December 1991.

Rewriting On Cyclic Structures: Equivalence Between The.. - Corradini, Gadducci (1999) (1 citation) (Correct)

.... also exists for other rule based formalisms like for example Petri nets , where the operational definition of, say, 50] parallels a categorical counterpart based on symmetric strict monoidal categories [45] and a logical one based on (the multiplicative fragment of) linear logic (see [43] for a survey) Much less satisfactory are the achievements of the theory of term graph rewriting, which has been studied by many authors, but only in operational style. In fact, term graphs have been represented as directed graphs satisfying a number of constraints [3] as suitable labelled ....

N. Mart'i-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. Int. Journal of Foundations of Computer Science, 4:297--399, 1991.

Axioms for Contextual Net Processes - Gadducci, Montanari (1998) (5 citations) (Correct)

....operational semantics of P T nets. Since P(N ) can be finitely axiomatized [26] this construction provides a finite axiomatization of non sequential processes. Moreover, the well understood setting of monoidal categories allows for an easy comparison with related models, like linear logic [17]. The aim of this paper is to extend the above categorical approach to P T nets with read arcs. Our results should enable a fully algebraic description and analysis of these nets and, as a consequence, of the concurrency paradigm based on shared memory they represent. To the best of our knowledge, ....

N. Mart'i-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. Int. Journal of Foundations of Computer Science, 4:297--399, 1991.

An Algebraic Presentation of Term Graphs, via GS-Monoidal.. - Corradini, Gadducci (1999) (1 citation) (Correct)

.... intention was to enrich symmetric monoidal categories in order to model a notion of local sharing: Our starting points were the already mentioned [33, 41] Next, in [14] when analysing two categorical models for term rewriting, we observed that neither the standard 2 categorical presentation of [46, 48] (see Section 6.4) nor the formulation based on the weaker notion of sesqui category by Stell [57, 59] were completely satisfactory from the perspective of a truly concurrent semantics. In fact, from that point of view, the equivalence on rewriting sequences (i.e. cells) holding in 2 categories ....

N. Mart'i-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. Int. Journal of Foundations of Computer Science, 4:297--399, 1991.

Rewriting on Cyclic Structures - Corradini, Gadducci (1998) (1 citation) (Correct)

.... also exists for other rule based formalisms, like for example Petri nets , where the operational definition of, say, 25] parallels a categorical counterpart based on symmetric strict monoidal categories [21] and a logical one based on (the multiplicative fragment of) linear logic (see [19] for a survey) The situation is not so lucky for term graph rewriting, which has been defined in the literature in many yet operational in flavour ways, representing term graphs for example as directed acyclic graphs satisfying a number of constraints [3] as suitable labelled hypergraphs ....

N. Mart'i-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. International Journal of Foundations of Computer Science, 4:297--399, 1991.

Research Directions in Rewriting Logic - Meseguer (1998) (10 citations) Self-citation (Meseguer) (Correct)

.... an apple and a quarter and a quarter, which is a strictly better situation than having an apple and a quarter (non idempotence of Omega ) Several researchers realized independently that this ACI operation on multisets corresponds to the conjunctive connective Omega (tensor) in linear logic [7, 161, 68, 103, 104]. This complementary point of view sees a net as a theory in this fragment of linear logic. Then, it is possible to establish a precise connection between reachability in Petri nets and provability in tensor logic. For example, in order to get the tensor theory corresponding to our Petri net ....

N. Mart'i-Oliet and J. Meseguer. From Petri nets to linear logic through categories: a survey. Intl. J. of Foundations of Comp. Sci., 2(4):297--399, 1991.

Rewriting Logic as a Unifying Framework for Petri Nets - Stehr, Meseguer, Csaba (2001) Self-citation (Meseguer) (Correct)

.... body of the paper, this work, including the abovementioned functorial semantics and the semantic equivalences, generalizes in some ways, and complements in others, a substantial body of work initiated by the second author in joint work with Ugo Montanari under the motto Petri nets are monoids [53, 45, 46, 56, 21, 54, 55, 57, 12, 13], in which categorical models are naturally associated as semantic models to Petri nets, and are shown to be equivalent to well known true concurrency models. Our work is also related to linear logic representations of Petri nets [45, 46, 4, 11, 10, 26] All this is not surprising, since, as ....

.... Petri nets are monoids [53, 45, 46, 56, 21, 54, 55, 57, 12, 13] in which categorical models are naturally associated as semantic models to Petri nets, and are shown to be equivalent to well known true concurrency models. Our work is also related to linear logic representations of Petri nets [45, 46, 4, 11, 10, 26]. All this is not surprising, since, as explained in [48] both the categorical place transition net models of [53] and the linear logic representations of place transition nets inspired rewriting logic as a generalization of both formalisms. But, as shown in this paper, the extra algebraic ....

[Article contains additional citation context not shown here]

N. Mart-Oliet and J. Meseguer. From Petri nets to linear logic through categories: A survey. International Journal of Foundations of Computer Science, 2(4):297-399, 1991.

A Concurrent Logical Framework: The Propositional.. - Watkins, Cervesato.. (2003) (2 citations) (Correct)