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Logic Programming with Focusing Proofs in Linear Logic
 Journal of Logic and Computation
, 1992
"... The deep symmetry of Linear Logic [18] makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and non symmetrical. I propose here one such model, in the area of Logic Programming, where the basic computational principle is C ..."
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Cited by 417 (8 self)
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The deep symmetry of Linear Logic [18] makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and non symmetrical. I propose here one such model, in the area of Logic Programming, where the basic computational principle is Computation = Proof search.
Petri Nets as Models of Linear Logic
 Proceedings of Colloquium on Trees in Algebra and Programming
, 1990
"... The chief purpose of this paper is to appraise the feasibility of Girard's linear logic as a specification language for parallel processes. To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic. 1 Intro ..."
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Cited by 34 (2 self)
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The chief purpose of this paper is to appraise the feasibility of Girard's linear logic as a specification language for parallel processes. To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the 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'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 nonnegative multiplicities forming a multiset of places, traditionally called a marking; as transitions occur, multipliciti...
The Coordination Language Facility: coordination of distributed objects
 JOURNAL OF THEORY AND PRACTICE OF OBJECT SYSTEMS (TAPOS
, 1996
"... The development of communication infrastructures and the rapid growth of networking facilities in information technologies increase information mobility and the decentralisation of work processes in industry and services. This evolution leads to increasing demands on the coordination of information ..."
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Cited by 22 (6 self)
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The development of communication infrastructures and the rapid growth of networking facilities in information technologies increase information mobility and the decentralisation of work processes in industry and services. This evolution leads to increasing demands on the coordination of information systems. However, information technologies available today are capable of supporting only interoperability of information systems from the point of view of communication infrastructures. This makes possible an easy exchange of information but provides no support for coordination. To fill this gap, we propose the Coordination Language Facility (CLF) as a coordination layer on top of distributed systems infrastructures such as CORBAcompliant Object Request Brokers. The CLF provides support for the coordination of heterogeneous, possibly distributed, active objects within larger units implementing (work) processes. On one hand, coordinator objects are declaratively implemented as rules. On the other hand, the objects participating in a coordination (participants) must instantiate a minimal interface which specifies the negotiation dialogue invoked, at runtime, by coordinators. The coordination activity is split between the implementation of the interface on the participants'side and the execution of the rules on the coordinators' side, thus offering a clear separation of concerns between local and global activities. The interface is specified using the CORBA standard for distributed objects, removing issues of heterogeneity and allowing each component to be implemented in the most appropriate language and environment.
Rewriting Logic as a Unifying Framework for Petri Nets
 Unifying Petri Nets, LNCS
, 2001
"... We propose rewriting logic as a unifying framework for a wide range of Petri nets models. We treat in detail place/transition nets and important extensions of the basic model by individual tokens, test arcs, and time. Based on the idea that "Petri nets are monoids" suggested by Meseguer an ..."
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Cited by 18 (7 self)
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We propose rewriting logic as a unifying framework for a wide range of Petri nets models. We treat in detail place/transition nets and important extensions of the basic model by individual tokens, test arcs, and time. Based on the idea that "Petri nets are monoids" suggested by Meseguer and Montanari we define a rewriting semantics that maps place/transition nets into rewriting logic specifications. We furthermore generalize this result to a general form of algebraic net specifications subsuming also colored Petri nets as a special case. The soundness and completeness results we state relate the commutative process semantics of Petri nets proposed by Best and Devillers to the modeltheoretic semantics of rewriting logic in the sense of natural isomorphisms between suitable functors. In addition we show how place/transition nets with test arcs and timed Petri nets can be equipped with a rewriting semantics and discuss how other extensions can be treated along similar lines.
Action and Change in Rewriting Logic
, 1996
"... Rewriting logic is proposed as a logic of concurrent action and change that solves the frame problem and that subsumes and unifies a number of previous logics of change, including linear logic and Horn logic with equality. Rewriting logic can represent action and change with great flexibility and ge ..."
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Cited by 12 (5 self)
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Rewriting logic is proposed as a logic of concurrent action and change that solves the frame problem and that subsumes and unifies a number of previous logics of change, including linear logic and Horn logic with equality. Rewriting logic can represent action and change with great flexibility and generality; this flexibility is illustrated by many examples, including examples that show how concurrent objectoriented systems are naturally represented. In addition, rewriting logic has a simple formalism, with only a few rules of deduction; it supports userdefinable logical connectives, which can be chosen to fit the problem at hand; it is intrinsically concurrent; and it is realizable in a wide spectrum logical language (Maude and its MaudeLog extension) supporting executable specification and programming. Contents 1 Introduction 2 1.1 What the frame problem (in our sense) is . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 What the frame problem (in our sense) is not . . . . . . ....
On the Structure of Highlevel Nets
 Helsinki University of Technology
, 1995
"... : The structure of Highlevel nets is studied from an algebraic and a logical point of view using Algebraic nets as an example. First the category of Algebraic nets is defined and the semantics given through an unfolding construction. Other kinds of Highlevel net formalisms are then presented. It is ..."
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Cited by 10 (0 self)
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: The structure of Highlevel nets is studied from an algebraic and a logical point of view using Algebraic nets as an example. First the category of Algebraic nets is defined and the semantics given through an unfolding construction. Other kinds of Highlevel net formalisms are then presented. It is shown that nets given in these formalisms can be transformed into equivalent Algebraic nets. Then the semantics of nets in terms of universal constructions is discussed. A definition of Algebraic nets in terms of structured transition systems is proposed. The semantics of the Algebraic net is then given as a free completion of this structured transition system to a category. As an alternative also a sheaf semantics of nets is examined. Here the semantics of the net arises as a limit of a diagram of sheaves. Next Algebraic nets are characterized as encodings of special morphisms called foldings. Each algebraic net gives rise to a surjective morphism between Petri nets and conversely each sur...
Logic and Fuzzy Petri Nets
"... This paper is a survey about theories capable of handling imprecision, uncertainty, resource management and evolution in time in dynamic systems such as manufacturing systems. The goal of this paper is twofold: i) discuss the relationship between the different types of logic (classical, fuzzy and li ..."
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Cited by 5 (0 self)
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This paper is a survey about theories capable of handling imprecision, uncertainty, resource management and evolution in time in dynamic systems such as manufacturing systems. The goal of this paper is twofold: i) discuss the relationship between the different types of logic (classical, fuzzy and linear) and Petri nets; ii) present and discuss the main fuzzy Petri nets models recently developed focusing on what elements are fuzzyfied. 1 Introduction Diagnosis and recovery procedures for dynamic discrete event systems, such as manufacturing systems, imply reasoning about objects and resources and their changing states. In addition it is necessary to deal with vague and uncertain data. Classical logic alone is not wellsuited for this task, particularly when change is concerned, the frame and ramification problem turns any classical reasoning difficult. Conversely, Petri nets are well suited to represent the states of a dynamic system made up of concurrent active objects sharing resourc...
On the Compositionality and Analysis of Algebraic HighLevel Nets
 RESEARCH REPORT A16, DIGITAL SYSTEMS LABORATORY
, 1991
"... This work discusses three aspects of net theory: compositionality of nets, analysis of nets and highlevel nets. Net theory has often been criticised for the difficulty of giving a compositional semantics to a net. In this work we discuss this problem form a category theoretic point of view. In cate ..."
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Cited by 3 (1 self)
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This work discusses three aspects of net theory: compositionality of nets, analysis of nets and highlevel nets. Net theory has often been criticised for the difficulty of giving a compositional semantics to a net. In this work we discuss this problem form a category theoretic point of view. In category theory compositionality is represented by colimits. We show how a highlevel net can be mapped into a lowlevel net that represents its behaviour. This construction is functorial and preserves colimits, giving a compositional semantics for these highlevel nets. Using this semantics we propose some proof rules for compositional reasoning with highlevel nets. Linear logic is a recently discovered logic that has many interesting properties. From a net theoretic point of view its interest lies in the fact that it is able to express resources in an analogous manner to nets. Several interpretations of Petri nets in terms of linear logic exist. In this work we study a model theoretic inter...
Acceptors as values: Functional programming in classical linear logic
, 1991
"... Girard’s linear logic has been previously applied to functional programming for performing statemanipulation and controlling storage reuse. These applications only use intuitionistic linear logic, the subset of linear logic that embeds intuitionistic logic. Full linear logic (called classical linea ..."
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Cited by 2 (1 self)
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Girard’s linear logic has been previously applied to functional programming for performing statemanipulation and controlling storage reuse. These applications only use intuitionistic linear logic, the subset of linear logic that embeds intuitionistic logic. Full linear logic (called classical linear logic) is much richer than this subset. In this paper, we consider the application of classical linear logic to functional programming. The negative types of linear logic are interpreted as denoting acceptors. An acceptor is an entity which takes an input of some type and returns no output. Acceptors generalize continuations and also single assignment variables, as found in data flow languages and logic programming languages. The parallel disjunction operator allows such acceptors to be used in a nontrivial fashion. Finally, the “why not ” operator of linear logic gives rise to nondeterministic values. We define a typed functional language based on the these ideas and demonstrate its use via examples. The language has a reduction semantics that generalizes typed lambda calculus, and satisfies strong normalization and ChurchRosser properties.