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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 10 (4 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 . . . . . . ....
Rewriting on Cyclic Structures
 Extended abstract in Fixed Points in Computer Science, satellite workshop of MFCS'98
, 1998
"... We present a categorical formulation of the rewriting of possibly cyclic term graphs, and the proof that this presentation is equivalent to the wellaccepted operational definition proposed in [3]  but for the case of circular redexes, for which we propose (and justify formally) a different treatm ..."
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Cited by 4 (3 self)
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We present a categorical formulation of the rewriting of possibly cyclic term graphs, and the proof that this presentation is equivalent to the wellaccepted operational definition proposed in [3]  but for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework, based on suitable 2categories, allows to model also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures. Furthermore, it can be used for defining various extensions of term graph rewriting, and for relating it to other rewriting formalisms.
Model Checking Linear Logic Specifications
, 2004
"... The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for specifications based on first order linear logic, a logic that can be used to naturally model infinite state systems with internal structured data. The fragment we consider in this ..."
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Cited by 4 (1 self)
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The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for specifications based on first order linear logic, a logic that can be used to naturally model infinite state systems with internal structured data. The fragment we consider in this paper is based on the linear logic programming language called LO [4] enriched with universally quantified goal formulas. Although LO was originally introduced as a theoretical foundation for extensions of logic programming languages, it can also be viewed as a very general language to specify a wide range of concurrent systems.
Petri Net Semantics of Bunched Implications
"... Engberg and Winskel's Petri net semantics of linear logic is reconsidered, from the point of view of the logic BI of bunched implications. We first show how BI can be used to overcome a number of difficulties pointed out by Engberg and Winskel, and we argue that it provides a more natural logic for ..."
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Engberg and Winskel's Petri net semantics of linear logic is reconsidered, from the point of view of the logic BI of bunched implications. We first show how BI can be used to overcome a number of difficulties pointed out by Engberg and Winskel, and we argue that it provides a more natural logic for the net semantics. We then briefly consider a more expressive logic based on an extension of BI with classical and modal features.
Branching processes of Petri nets in the context of the "nets in nets" paradigm
, 2000
"... Object Petri nets are one approach to the investigation of objectorientation and concurrency. We like to relate some work done in the area of the possible semantics for some classes of object Petri nets to the notations used for process calculi in the Milner style and to some algebraic foundations. ..."
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Object Petri nets are one approach to the investigation of objectorientation and concurrency. We like to relate some work done in the area of the possible semantics for some classes of object Petri nets to the notations used for process calculi in the Milner style and to some algebraic foundations. This algebra reveals some insights to the connections between the reference and the value semantics. We also hope, that this approach helps to unify rewriting systems with the theories on the description of processes of Petri nets and also with the theory of process algebra in a simple way.
Branching processes of Petri nets an unifying approach
"... Object Petri nets are one approach to the investigation of objectorientation and concurrency. We like to relate some work done in the area of the possible semantics for some classes of object Petri nets to the notations used for process calculi in the Milner style and to some algebraic foundations. ..."
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Object Petri nets are one approach to the investigation of objectorientation and concurrency. We like to relate some work done in the area of the possible semantics for some classes of object Petri nets to the notations used for process calculi in the Milner style and to some algebraic foundations. This algebra reveals some insights to the connections between the reference and the value semantics. We also hope, that this approach helps to unify rewriting systems with the theories on the description of processes of Petri nets and also with the theory of process algebra in a simple way.
Termination
"... proof. Let us examine why. ; #M 1 :A 2#A 1 2 :A 2 #E. M 2 :A 1 We can make the following inferences. V 1 = #x:A 2 .M # 1 By type preservation and inversion At this point we cannot proceed: we need a derivation of [V 2 /x]M # 1 ## V for some V to complete the derivation of M 1 ..."
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proof. Let us examine why. ; #M 1 :A 2#A 1 2 :A 2 #E. M 2 :A 1 We can make the following inferences. V 1 = #x:A 2 .M # 1 By type preservation and inversion At this point we cannot proceed: we need a derivation of [V 2 /x]M # 1 ## V for some V to complete the derivation of M 1 M 2 ## V . Unfortunately, the induction hypothesis does not tell us anything about [V 2 /x]M # 1 . Basically, we need to extend it so it makes a statement about the result of evaluation ( #x:A 2 .M # 1 ,inthis case). Sticking to the case of linear application for the moment, we call a term M "good" if it evaluates to a "good" value V .AvalueVis "good" if it is a function #x:A 2 .M # 1 and if substituting a "good" value V 2 for x in M # 1 results in a "good" term. Note that this is not a proper definition, since to see if V is "good" we may need to substitute any "good" value V 2 into it, possibly including V itself. We can make this definition inductive if we observe that the value