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126
Ontology Mapping: The State of the Art
, 2003
"... Ontology mapping is seen as a solution provider in today's landscape of ontology research. As the number of ontologies that are made publicly available and accessible on the Web increases steadily, so does the need for applications to use them. A single ontology is no longer enough to support the ta ..."
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Cited by 305 (9 self)
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Ontology mapping is seen as a solution provider in today's landscape of ontology research. As the number of ontologies that are made publicly available and accessible on the Web increases steadily, so does the need for applications to use them. A single ontology is no longer enough to support the tasks envisaged by a distributed environment like the Semantic Web. Multiple ontologies need to be accessed from several applications. Mapping could provide a common layer from which several ontologies could be accessed and hence could exchange information in semantically sound manners. Developing such mappings has been the focus of a variety of works originating from diverse communities over a number of years. In this article we comprehensively review and present these works. We also provide insights on the pragmatics of ontology mapping and elaborate on a theoretical approach for defining ontology mapping.
OrderSorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations
 Theoretical Computer Science
, 1992
"... This paper generalizes manysorted algebra (hereafter, MSA) to ordersorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of objectoriented programming), several forms of pol ..."
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Cited by 208 (33 self)
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This paper generalizes manysorted algebra (hereafter, MSA) to ordersorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of objectoriented programming), several forms of polymorphism and overloading, partial operations (as total on equationally defined subsorts), exception handling, and an operational semantics based on term rewriting. We give the basic algebraic constructions for OSA, including quotient, image, product and term algebra, and we prove their basic properties, including Quotient, Homomorphism, and Initiality Theorems. The paper's major mathematical results include a notion of OSA deduction, a Completeness Theorem for it, and an OSA Birkhoff Variety Theorem. We also develop conditional OSA, including Initiality, Completeness, and McKinseyMalcev Quasivariety Theorems, and we reduce OSA to (conditional) MSA, which allows lifting many known MSA results to OSA. Retracts, which intuitively are left inverses to subsort inclusions, provide relatively inexpensive runtime error handling. We show that it is safe to add retracts to any OSA signature, in the sense that it gives rise to a conservative extension. A final section compares and contrasts many different approaches to OSA. This paper also includes several examples demonstrating the flexibility and applicability of OSA, including some standard benchmarks like STACK and LIST, as well as a much more substantial example, the number hierarchy from the naturals up to the quaternions.
Metalogical Frameworks
, 1992
"... In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the me ..."
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Cited by 57 (15 self)
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In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the metalogic of the object language being implemented. We also reason about the implementation itself, say to know it is correct; this is done in a programming logic. How do all these logics relate? This paper considers that question and more. We show that by taking the view that the metalogic is primary, these other parts are related in standard ways. The metalogic should be suitably rich so that the object logic can be presented as an abstract data type, and it must be suitably computational (or constructive) so that an instance of that type is an implementation. The data type abstractly encodes all that is relevant for metareasoning, i.e., not only the term constructing functions but also the...
Moving Between Logical Systems
 Recent Trends in Data Type Specification
, 1998
"... : This paper presents a number of concepts of a mapping between logical systems modelled as institutions, discusses their mutual merits and demerits, and sketches their role in the process of system specification and development. Some simple properties of the resulting categories of institutions are ..."
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Cited by 50 (3 self)
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: This paper presents a number of concepts of a mapping between logical systems modelled as institutions, discusses their mutual merits and demerits, and sketches their role in the process of system specification and development. Some simple properties of the resulting categories of institutions are given. 1 Introduction We have to live with a multitude of logical systems used in various approaches to software specification and development. The proliferation of logical systems in the area is not just researchers' fancy, but results from the very practical needs to capture various aspects of software systems and to cater for various programming paradigms. Each of them leads to a different notion of a semantic model capturing the semantic essence of the adopted view of software systems. For instance, standard (manysorted) algebras [BL70], [GTW78] provide a satisfactory framework for modelling data types where all operations always yield welldefined results. However, if general recursi...
Reasoning Theories  Towards an Architecture for Open Mechanized Reasoning Systems
, 1994
"... : Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be ..."
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Cited by 47 (11 self)
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: Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be based on different logics; have different domain models; use different vocabularies and data structures; use different reasoning strategies; and have different interaction capabilities. This paper makes two main contributions towards our goal. First, it proposes a general architecture for a class of reasoning systems called Open Mechanized Reasoning Systems (OMRSs). An OMRS has three components: a reasoning theory component which is the counterpart of the logical notion of formal system, a control component which consists of a set of inference strategies, and an interaction component which provides an OMRS with the capability of interacting with other systems, including OMRSs and hum...
Towards an Evolutionary Formal Software Development
 Proceedings Workshop on Algebraic Development Techniques, WADT99. Springer, LNCS 1827
, 1999
"... Although formal methods have been successfully applied in various industrial applications, their use in software development is still restricted to individual case studies. To overcome this situation we aim at a methodology for an evolutionary formal software development which allows for a stepwise ..."
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Cited by 37 (8 self)
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Although formal methods have been successfully applied in various industrial applications, their use in software development is still restricted to individual case studies. To overcome this situation we aim at a methodology for an evolutionary formal software development which allows for a stepwise and incremental development process along the line of rapid prototyping. The approach is based on work on a formal management of change for formal developments which is able to maintain proofs when changing specifications.
Semantic Lego
, 1995
"... Denotational semantics [Sch86] is a powerful framework for describing programming languages; however, its descriptions lack modularity: conceptually independent language features influence each others' semantics. We address this problem by presenting a theory of modular denotational semantics. Follo ..."
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Cited by 36 (0 self)
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Denotational semantics [Sch86] is a powerful framework for describing programming languages; however, its descriptions lack modularity: conceptually independent language features influence each others' semantics. We address this problem by presenting a theory of modular denotational semantics. Following Mosses [Mos92], we divide a semantics into two parts, a computation ADT and a language ADT (abstract data type). The computation ADT represents the basic semantic structure of the language. The language ADT represents the actual language constructs, as described by a grammar. We define the language ADT using the computation ADT; in fact, language constructs are polymorphic over many different computation ADTs. Following Moggi [Mog89a], we build the computation ADT from composable parts, using monads and monad transformers. These techniques allow us to build many different computation ADTs, and, since our language constructs are polymorphic, many different language semantics. We autom...
Axiomatizing Reflective Logics and Languages
 Proceedings of Reflection'96
, 1996
"... The very success and breadth of reflective techniques underscores the need for a general theory of reflection. At present what we have is a wideranging variety of reflective systems, each explained in its own idiosyncratic terms. Metalogical foundations can allow us to capture the essential aspects ..."
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Cited by 35 (20 self)
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The very success and breadth of reflective techniques underscores the need for a general theory of reflection. At present what we have is a wideranging variety of reflective systems, each explained in its own idiosyncratic terms. Metalogical foundations can allow us to capture the essential aspects of reflective systems in a formalismindependent way. This paper proposes metalogical axioms for reflective logics and declarative languages based on the theory of general logics [34]. In this way, several strands of work in reflection, including functional, equational, Horn logic, and rewriting logic reflective languages, as well as a variety of reflective theorem proving systems are placed within a common theoretical framework. General axioms for computational strategies, and for the internalization of those strategies in a reflective logic are also given. 1 Introduction Reflection is a fundamental idea. In logic it has been vigorously pursued by many researchers since the fundamental wor...
Maude as a Formal MetaTool
 FM’99 — Formal Methods, World Congress on Formal Methods in the Development of Computing Systems
, 1999
"... 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 a ..."
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Cited by 34 (13 self)
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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 metatools 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 logicindependent, but that at present require costly implementation efforts for each formalism, could be provided for logics in general by module algebra generator metatools. The foundations of metatools 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 metatools 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
The Heterogeneous Tool Set
 of Lecture Notes in Computer Science
, 2007
"... 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 resea ..."
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Cited by 30 (21 self)
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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 adhoc 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 multilogic specification. Hets is based on a graph of logics and languages (formalized as socalled 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 largescale 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