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39
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 82 (22 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...
Integrating computer algebra into proof planning
 Journal of Automated Reasoning
, 1998
"... Abstract. Mechanised reasoning systems and computer algebra systems have different objectives. Their integration is highly desirable, since formal proofs often involve both of the two di erent tasks, proving and calculating. Even more importantly, proof and computation are often interwoven and not e ..."
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Cited by 41 (26 self)
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Abstract. Mechanised reasoning systems and computer algebra systems have different objectives. Their integration is highly desirable, since formal proofs often involve both of the two di erent tasks, proving and calculating. Even more importantly, proof and computation are often interwoven and not easily separable. In this contribution we advocate an integration of computer algebra into mechanised reasoning systems at the proof plan level. This approach allows to view the computer algebra algorithms as methods, that is, declarative representations of the problem solving knowledge speci c to a certain mathematical domain. Automation can be achieved in many cases bysearching for a hierarchic proof plan at the methodlevel using suitable domainspeci c control knowledge about the mathematical algorithms. In other words, the uniform framework of proof planning allows to solve a large class of problems that are not automatically solvable by separate systems. Our approach also gives an answer to the correctness problems inherent insuch an integration. We advocate an approach where the computer algebra system produces highlevel protocol information that can be processed by aninterface to derive proof plans. Such a proof plan in turn can be expanded to proofs at di erent levels of abstraction, so the approach iswellsuited for producing a highlevel verbalised explication as well as for a lowlevel machine checkable calculuslevel proof. We present an implementation of our ideas and exemplify them using an automatically solved example. Changes in the criterion of `rigour of the proof ' engender major revolutions in mathematics.
ΩANTS  An open approach at combining Interactive and Automated Theorem Proving
 IN PROC. OF CALCULEMUS2000. AK PETERS
, 2000
"... We present the ΩAnts theorem prover that is built on top of an agentbased command suggestion mechanism. The theorem prover inherits beneficial properties from the underlying suggestion mechanism such as runtime extendibility and resource adaptability. Moreover, it supports the distributed integ ..."
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Cited by 35 (23 self)
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We present the ΩAnts theorem prover that is built on top of an agentbased command suggestion mechanism. The theorem prover inherits beneficial properties from the underlying suggestion mechanism such as runtime extendibility and resource adaptability. Moreover, it supports the distributed integration of external reasoning systems. We also introduce some notions that need to be considered to check completeness and soundness of such a system with respect to an underlying calculus.
Specification and Integration of Theorem Provers and Computer Algebra Systems
 Fundamenta Informaticae
"... Computer algebra systems (CASs) and automated theorem provers (ATPs) exhibit complementary abilities. CASs focus on efficiently solving domainspecific problems. ATPs are designed to allow for the formalization and solution of wide classes of problems within some logical framework. Integrating C ..."
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Cited by 27 (14 self)
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Computer algebra systems (CASs) and automated theorem provers (ATPs) exhibit complementary abilities. CASs focus on efficiently solving domainspecific problems. ATPs are designed to allow for the formalization and solution of wide classes of problems within some logical framework. Integrating CASs and ATPs allows for the solution of problems of a higher complexity than those confronted by each class alone. However, most experiments conducted so far followed an adhoc approach, resulting in tailored solutions to specific problems. A structured and principled approach is necessary to allow for the sound integration of systems in a modular way. The Open Mechanized Reasoning Systems (OMRS) framework was introduced for the specification and implementation of mechanized reasoning systems, e.g. ATPs. The approach was recasted to the domain of computer algebra systems. In this paper, we introduce a generalization of OMRS, named OMSCS (Open Mechanized Symbolic Computation Systems). We show how OMSCS can be used to soundly express CASs, ATPs, and their integration, by formalizing a combination between the Isabelle prover and the Maple algebra system. We show how the integrated system solves a problem which could not be tackled by each single system alone.
AgentOriented Integration of Distributed Mathematical Services
 Journal of Universal Computer Science
, 1999
"... Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that ..."
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Cited by 19 (10 self)
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Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that a reasonable framework for automated theorem proving in the large regards typical mathematical services as autonomous agents that provide internal functionality to the outside and that, in turn, are able to access a variety of existing external services. This article describes...
Constraint Contextual Rewriting
, 1998
"... We are interested in the problem of integrating decision procedures with rewriting as in many stateoftheart verication systems. We dene Constraint Contextual Rewriting (CCR) as a generalization of contextual rewriting, whereby the rewriting context is processed by the available decision proced ..."
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Cited by 17 (6 self)
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We are interested in the problem of integrating decision procedures with rewriting as in many stateoftheart verication systems. We dene Constraint Contextual Rewriting (CCR) as a generalization of contextual rewriting, whereby the rewriting context is processed by the available decision procedures. We show how CCR accounts for some of the most important integration schemas adopted in stateoftheart veri cation systems. The rulebased presentation of CCR given in this paper contrasts the practice of describing the integration either by examples or in informal ways with highlevel ideas intermixed with implementation details. Important properties (e.g. soundness) of the proposed integration schema can be formally stated and proved. Moreover, the approach is amenable of operationalization. This has allowed us to easily fastprototype and validate the integration schemas described in this paper.
Integrating Computer Algebra with Proof Planning
, 1996
"... . Mechanised reasoning systems and computer algebra systems have apparently different objectives. Their integration is, however, highly desirable, since in many formal proofs both of the two different tasks, proving and calculating, have to be performed. In the context of producing reliable proofs, ..."
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Cited by 15 (6 self)
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. Mechanised reasoning systems and computer algebra systems have apparently different objectives. Their integration is, however, highly desirable, since in many formal proofs both of the two different tasks, proving and calculating, have to be performed. In the context of producing reliable proofs, the question how to ensure correctness when integrating a computer algebra system into a mechanised reasoning system is crucial. In this contribution, we discuss the correctness problems that arise from such an integration and advocate an approach in which the calculations of the computer algebra system are checked at the calculus level of the mechanised reasoning system. We present an implementation which achieves this by adding a verbose mode to the computer algebra system which produces highlevel protocol information that can be processed by an interface to derive proof plans. Such a proof plan in turn can be expanded to proofs at different levels of abstraction, so the approach is well...
Structures for Symbolic Mathematical Reasoning and Computation
 DESIGN AND IMPLEMENTATION OF SYMBOLIC COMPUTATION SYSTEMS, DISCO'96, NUMBER1128 IN LNCS
, 1996
"... Recent research towards integrating symbolic mathematical reasoning and computation has led to prototypes of interfaces and environments. This paper introduces computation theories and structures to represent mathematical objects and applications of algorithms occuring in algorithmic services. The ..."
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Cited by 15 (5 self)
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Recent research towards integrating symbolic mathematical reasoning and computation has led to prototypes of interfaces and environments. This paper introduces computation theories and structures to represent mathematical objects and applications of algorithms occuring in algorithmic services. The composition of reasoning and computation theories and structures provide a formal framework for the specification of symbolic mathematical problem solving by cooperation of algorithms and theorems.
A Provably Correct Embedded Verifier for the Certification of Safety . . .
, 1997
"... vframe is one of Ansaldo's software driven vital architectures for safety critical products. This paper describes a project whose result is the development of an "embedded verifier", i.e. a system integrated within vframe and able to certify the correctness of one of vframe components, a compiler. ..."
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Cited by 14 (1 self)
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vframe is one of Ansaldo's software driven vital architectures for safety critical products. This paper describes a project whose result is the development of an "embedded verifier", i.e. a system integrated within vframe and able to certify the correctness of one of vframe components, a compiler. The embedded verifier satisfies two precise requirements. First, the compiler must be certified in a fully automatic and efficient way. Second, the embedded verifier must be itself certified, in a way which can be easily understood and validated by end users.
Towards interoperable mechanized reasoning systems: the logic broker architecture
 AI*IATABOO Workshop `From Objects to Agents: Evolutionary Trends of Software Systems
, 2000
"... There is a growing interest in the integration of mechanized reasoning systems such as automated theorem provers, computer algebra systems, and model checkers. Stateoftheart reasoning systems are the result of many manyears of careful development and engineering, and usually they provide a high ..."
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Cited by 14 (1 self)
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There is a growing interest in the integration of mechanized reasoning systems such as automated theorem provers, computer algebra systems, and model checkers. Stateoftheart reasoning systems are the result of many manyears of careful development and engineering, and usually they provide a high degree of sophistication in their respective domain. Yet they often perform poorly when applied outside the domain they have been designed for. The problem of integrating mechanized reasoning systems is therefore being perceived as an important issue in automated reasoning. In this paper we present the Logic Broker Architecture, a framework which provides the needed infrastructure for making mechanized reasoning systems interoperate. The architecture provides location transparency, a way to forward requests for logical services to appropriate reasoning systems via a simple registration/subscription mechanism, and a translation mechanism which ensures the transparent and provably sound exchange of logical services. 1