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Rewriting Logic as a Semantic Framework for Concurrency: a Progress Report
, 1996
"... . This paper surveys the work of many researchers on rewriting logic since it was first introduced in 1990. The main emphasis is on the use of rewriting logic as a semantic framework for concurrency. The goal in this regard is to express as faithfully as possible a very wide range of concurrency mod ..."
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Cited by 86 (24 self)
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. This paper surveys the work of many researchers on rewriting logic since it was first introduced in 1990. The main emphasis is on the use of rewriting logic as a semantic framework for concurrency. The goal in this regard is to express as faithfully as possible a very wide range of concurrency models, each on its own terms, avoiding any encodings or translations. Bringing very different models under a common semantic framework makes easier to understand what different models have in common and how they differ, to find deep connections between them, and to reason across their different formalisms. It becomes also much easier to achieve in a rigorous way the integration and interoperation of different models and languages whose combination offers attractive advantages. The logic and model theory of rewriting logic are also summarized, a number of current research directions are surveyed, and some concluding remarks about future directions are made. Table of Contents 1 In...
Ordered Chaining Calculi for FirstOrder Theories of Transitive Relations
 Journal of the ACM
, 1998
"... this paper have been presented at the 12th International Conference on Automated Deduction (Nancy, France, June/July 1994) and the 9th IEEE Symposium on Logic in Computer Science (Paris, France, July 1994). ..."
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Cited by 33 (4 self)
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this paper have been presented at the 12th International Conference on Automated Deduction (Nancy, France, June/July 1994) and the 9th IEEE Symposium on Logic in Computer Science (Paris, France, July 1994).
Birewrite systems
, 1996
"... In this article we propose an extension of term rewriting techniques to automate the deduction in monotone preorder theories. To prove an inclusion a ⊆ b from a given set I of them, we generate from I, using a completion procedure, a birewrite system 〈R⊆, R⊇〉, that is, a pair of rewrite relations ..."
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Cited by 30 (8 self)
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In this article we propose an extension of term rewriting techniques to automate the deduction in monotone preorder theories. To prove an inclusion a ⊆ b from a given set I of them, we generate from I, using a completion procedure, a birewrite system 〈R⊆, R⊇〉, that is, a pair of rewrite relations −−− → R ⊆ and −−− → R ⊇ , and seek a common term c such that a −−−→ R ⊆ c and b −−−→
Ordered Chainings for Total Orderings
, 1995
"... We design new inference systems for total orderings by applying rewrite techniques to chaining calculi. Equality relations may either be specified axiomatically or built into the deductive calculus via paramodulation or superposition. We demonstrate that our inference systems are compatible with ..."
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Cited by 25 (7 self)
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We design new inference systems for total orderings by applying rewrite techniques to chaining calculi. Equality relations may either be specified axiomatically or built into the deductive calculus via paramodulation or superposition. We demonstrate that our inference systems are compatible with a concept of (global) redundancy for clauses and inferences that covers such widely used simplification techniques as tautology deletion, subsumption, and demodulation. A key to the practicality of chaining techniques is the extent to which socalled variable chainings can be restricted. Syntactic ordering restrictions on terms and the rewrite techniques which account for their completeness considerably restrict variable chaining. We show that variable elimination is an admissible simplification techniques within our redundancy framework, and that consequently for dense total orderings without endpoints no variable chaining is needed at all.
Algebraic Approaches to Nondeterminism  an Overview
 ACM Computing Surveys
, 1997
"... this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University ..."
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Cited by 22 (3 self)
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this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University
Towards Specifying with Inclusions
, 1997
"... In this article we present a functional specification language based on inclusions between set expressions. Instead of computing with data individuals we deal with their classification into sets. The specification of functions and relations by means of inclusions can be considered as a generalizatio ..."
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Cited by 5 (2 self)
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In this article we present a functional specification language based on inclusions between set expressions. Instead of computing with data individuals we deal with their classification into sets. The specification of functions and relations by means of inclusions can be considered as a generalization of the conventional algebraic specification by means of equations. The main aim of this generalization is to facilitate the incremental refinement of specifications. Furthermore, inclusional specifications admit a natural visual syntax which can also be used to visualize the reasoning process. We show that reasoning with inclusions is well captured by birewriting, a rewriting technique introduced by Levy and Agust'i [15]. However, there are still key problems to be solved in order to have executable inclusional specifications, necessary for rapid prototyping purposes. The article mainly points to the potentialities and difficulties of specifying with inclusions.
NonSymmetric Rewriting
, 1996
"... Rewriting is traditionally presented as a method to compute normal forms in varieties. Conceptually, however, its essence are commutation properties. We develop rewriting as a general theory of commutation for two possibly nonsymmetric transitive relations modulo a congruence and prove a general ..."
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Cited by 5 (5 self)
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Rewriting is traditionally presented as a method to compute normal forms in varieties. Conceptually, however, its essence are commutation properties. We develop rewriting as a general theory of commutation for two possibly nonsymmetric transitive relations modulo a congruence and prove a generalization of the standard ChurchRosser theorem. The theorems of equational rewriting, including the existence of normal forms, derive as corollaries to this result. Completion also is purely commutational and we show how to extend it to plain transitive relations. Nevertheless the loss of symmetry introduces some unpleasant consequences: unique normal forms do not exist, rewrite proofs cannot be found by don'tcare nondeterministic rewriting and also simplification during completion requires backtracking. On the nonground level, variable critical pairs have to be considered. Keywords Transitive Relations, Rewriting, Commutation, Completion. 1 Introduction Term rewriting is one of t...
Query Answering by Means of Diagram Transformation
, 1998
"... In previous work we presented a diagrammatic syntax for logic programming which clearly `resembles' the semantics of predicates as relations, i.e. sets of tuples in the Universe of Discourse. This paper shows diagrams as an alternative formal notation for pure logic programming which not only e ..."
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Cited by 3 (1 self)
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In previous work we presented a diagrammatic syntax for logic programming which clearly `resembles' the semantics of predicates as relations, i.e. sets of tuples in the Universe of Discourse. This paper shows diagrams as an alternative formal notation for pure logic programming which not only emphasizes some structural features of logical statements, but could also be useful to conduct visual inferences and to communicate them. This paper describes the current state of our research on a visual inference system for answering visually posed queries by means of diagram transformations. Although the transformations are shown by example we point to their correctness and formal character.
Visual Logic Programming through Set Inclusion and Chaining
 IN CADE13 WORKSHOP ON VISUAL REASONING
, 1996
"... ..."
From Queries to Answers in Visual Logic Programming
 PROCEEDINGS OF VL'97, SEPTEMBER 2326, 1997 IN CAPRI, ITALY
, 1997
"... In VL'96 we presented a visual declarative programming language based on two main graphical constructs: directed acyclic graphs representing predicate application and graphical set inclusion representing logical implication. We showed that with these simple visual constructs we can cover most o ..."
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Cited by 3 (1 self)
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In VL'96 we presented a visual declarative programming language based on two main graphical constructs: directed acyclic graphs representing predicate application and graphical set inclusion representing logical implication. We showed that with these simple visual constructs we can cover most of the representational demands of computational logic allowing a blend of functional and relational styles of programming. In this paper we explore the advantages of using directly our visual syntax for solving queries, by giving a way to visually ask questions about a visual program by means of query diagrams, and by defining visual inferences which operate on those diagrams. The result is an operational semantics for declarative programming which is intended to be visual, intuitive and formal. Visual because the inference rules display graphically the transformation of query diagrams into answer diagrams. Intuitive because it is intimately linked with the visual syntax of the declarative language. Finally it is formal because the usual properties of formal logic (i.e. correctness and completeness) can be applied directly to it.