This paper explains the design and use of two equational proving tools, namely an inductive theorem prover -- to prove theorems about equational specifications with an initial algebra semantics -- and a Church-Rosser checker---to check whether such specifications satisfy the Church-Rosser property. These tools can be used to prove properties of order-sorted equational specifications in Cafe [11] and of membership equational logic specifications in Maude [7, 6]. The tools have been written entirely in Maude and are in fact executable specifications in rewriting logic of the formal inference systems that they implement.

Given the different perspectives from which a complex software system has to be analyzed, the multiplicity of formalisms is unavoidable. This poses two important technical challenges: how to rigorously meet the need to interrelate formalisms, and how to reduce the duplication of effort in tool and specification building across formalisms. These challenges could be answered by adequate formal meta-tools that, when given the specification of a formal inference system, generate an efficient inference engine, and when given a specification of two formalisms and a translation, generate an actual translator between them. Similarly, module composition operations that are logic-independent, but that at present require costly implementation efforts for each formalism, could be provided for logics in general by module algebra generator meta-tools. The foundations of meta-tools of this kind can be based on a metatheory of general logics. Their actual design and implementation can be based on appropriate logical frameworks having efficient implementations. This paper explains how the reflective logical framework of rewriting logic can be used, in conjunction with an efficient reflective implementation such as the Maude language, to design formal meta-tools such as those described above. The feasibility of these ideas and techniques has been demonstrated by a number of substantial experiments in which new formal tools and new translations between formalisms, efficient enough to be used in practice, have been generated. 1

Component-based software development is gaining recognition as the key technology for the construction of high-quality, evolvable, large software systems in timely and affordable manners. In this new setting, interoperability is one of the essential issues, since it enables the composition of reusable heterogeneous components developed by different people, at different times, and possibly with different uses in mind. Currently most object and component platforms (such as CORBA, DCOM, or EJB) already provide the basic infrastructure for component interoperability at the lower levels, i.e., they sort out most of the "plumbing" issues. However, interoperability goes far beyond that; it also involves behavioral compatibility, protocol compliance, agreements on the business rules, etc. This chapter tries to go through the basic concepts related to component interoperability, with special emphasis in the syntactic, protocol and operational specifications of components. Our main goal is to point out the existing problems, survey the current solutions and how they address those problems, and to draw attention towards some of the still open issues and challenges in this interesting research area.

Abstract. Heterogeneous specification becomes more and more important because complex systems are often specified using multiple viewpoints, involving multiple formalisms. Moreover, a formal software development process may lead to a change of formalism during the development. However, current research in integrated formal methods only deals with ad-hoc integrations of different formalisms. The heterogeneous tool set (Hets) is a parsing, static analysis and proof management tool combining various such tools for individual specification languages, thus providing a tool for heterogeneous multi-logic specification. Hets is based on a graph of logics and languages (formalized as so-called institutions), their tools, and their translations. This provides a clean semantics of heterogeneous specification, as well as a corresponding proof calculus. For proof management, the calculus of development graphs (known from other large-scale proof management systems) has been adapted to heterogeneous specification. Development graphs provide an overview of the (heterogeneous) specification module hierarchy and the current proof state, and thus may be used for monitoring the overall correctness of a heterogeneous development. 1

The emergent Semantic Web, despite being in its infancy, has already received a lot of attention from academia and industry. This resulted in an abundance of prototype systems and discussion most of which are centred around the underlying infrastructure. However, when we critically review the work done to date we realise that there is little discussion with respect to the vision of the Semantic Web. In particular, there is an observed dearth of discussion on how to deliver knowledge sharing in an environment such as the Semantic Web in effective and efficient manners. There are a lot of overlooked issues, associated with agents and trust to hidden assumptions made with respect to knowledge representation and robust reasoning in a distributed environment. These issues could potentially hinder further development if not considered at the early stages of designing Semantic Web systems. In this perspectives' paper, we aim to help engineers and practitioners of the Semantic Web by raising awareness of these issues.

Recently, as part of a general formal (i.e. logic based) methodology for mathematical knowledge management we also introduced a method for the automated synthesis of correct algorithms, which we called the lazy thinking method. For a given concrete problem specification (in predicate logic), the method tries out various algorithm schemes and derives specifications for the subalgorithms in the algorithm scheme.

Our thesis is that before Web-based agents can negotiate meanings, they need to agree on high-level protocols based on logical systems. The Semantic Web community is setting the stage for semantic interoperability among Web-based software agents by developing standard languages with well-defined semantics. But exactly how these languages might be used to negotiate meanings is an open question.

Data Type Specification, in combination with modal logics for formalizing the process of building systems from interconnected components. This combination of logical and categorical techniques has also been applied to parallel program design languages in the style of UNITY [14] and IP [41], providing semantics for modularization techniques based on the notion of superposition. This has resulted in the development of a programming design language called Community [33]. Two formalisms that provide explicit support for object systems and can reason about their rewriting logic specifications have been recently developed. One is a version of the modal -calculus proposed by Lechner [48, 49] for reasoning about object-oriented Maude specifications. Another is Denker's objectoriented distributed temporal logic DTL + [24, 22], that extends the DTL and D 1 distributed object temporal logics of Ehrich and Denker [30, 23, 29]. Lechner [48, 49] uses her version of the modal -calculus to identif...

Abstract. An algebraic approach to the view consistency problem in software development is provided. A view is formalised as a sentence of a viewpoint language; a viewpoint is given by a language and its semantics. Views in possibly different viewpoints are compared over a common view for consistency by a heterogenous pull-back construction. This general notion of view consistency is illustrated by several examples from viewpoints used in object-oriented software development. 1

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