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Rewriting Logic as a Logical and Semantic Framework
, 1993
"... Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are und ..."
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Cited by 157 (54 self)
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Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are understood as mappings L ! F that translate one logic into the other in a conservative way. The ease with which such maps can be defined for a number of quite different logics of interest, including equational logic, Horn logic with equality, linear logic, logics with quantifiers, and any sequent calculus presentation of a logic for a very general notion of "sequent," is discussed in detail. Using the fact that rewriting logic is reflective, it is often possible to reify inside rewriting logic itself a representation map L ! RWLogic for the finitely presentable theories of L. Such a reification takes the form of a map between the abstract data types representing the finitary theories of...
A Calculus of Transformation

, 1994
"... This paper presents the concepts and the semantics of a transformationcalculus TC that is generic wrt. concrete object languages. Built upon an object language description given by theory in higherorder logics (see [Andr 86]), TC provides contextsensitive rules in which requirements on the conte ..."
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Cited by 13 (7 self)
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This paper presents the concepts and the semantics of a transformationcalculus TC that is generic wrt. concrete object languages. Built upon an object language description given by theory in higherorder logics (see [Andr 86]), TC provides contextsensitive rules in which requirements on the context of a redex can be imposed, and integrates a restricted form of extended rewriting. Furthermore, rules may be higherorder in order to represent tactical combinators and to model "parametric transformations". This work can be seen as a specification of transformation systems and a foundation for correctnessproofs of transformations.
Context Institutions
, 1996
"... . The paper introduces a notion of a context institution. The notion is explicitly illustrated by two standard examples. Morphism between context institutions are introduced, thus yielding a category of context institutions. Some expected constructions on context institutions are presented as functo ..."
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Cited by 7 (2 self)
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. The paper introduces a notion of a context institution. The notion is explicitly illustrated by two standard examples. Morphism between context institutions are introduced, thus yielding a category of context institutions. Some expected constructions on context institutions are presented as functors from this category. The potential usefulness of these notions is illustrated by one such a construction, yielding a Hoare logic for an arbitrary small context institution satisfying mild extra assumptions. 1 Introduction The theory of institutions ([4], [6]) has proved its usefulness in the area of foundations of software specification and development. The modeltheoretic view of logical systems advocated in the theory of institutions captures very well the idea that in computer science applications of logic what we are really interested in are models. We always try to specify (logical) properties of concrete objects standard examples can be programs, database management systems or ...
Grothendieck Inclusion Systems
 APPLIED CATEGORICAL STRUCTURES
"... Inclusion systems have been introduced in algebraic specification theory as a categorical structure supporting the development of a general abstract logicindependent approach to the algebra of specification (or programming) modules. Here we extend the concept of indexed categories and their Grothe ..."
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Cited by 1 (1 self)
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Inclusion systems have been introduced in algebraic specification theory as a categorical structure supporting the development of a general abstract logicindependent approach to the algebra of specification (or programming) modules. Here we extend the concept of indexed categories and their Grothendieck flattenings to inclusion systems. An important practical significance of the resulting Grothendieck inclusion systems is that they allow the development of module algebras for multilogic heterogeneous specification frameworks. At another level, we show that several inclusion systems in use in some syntactic (signatures, deductive theories) or semantic contexts (models) appear as Grothendieck inclusion systems too. We also study several general properties of Grothendieck inclusion systems.
An Axiomatic Approach to Structuring Specifications
"... In this paper we develop an axiomatic approach to structured specifications in which both the underlying logical system and corresponding institution of the structured specifications are treated as abstract institutions, which means two levels of institution independence. This abstract axiomatic app ..."
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In this paper we develop an axiomatic approach to structured specifications in which both the underlying logical system and corresponding institution of the structured specifications are treated as abstract institutions, which means two levels of institution independence. This abstract axiomatic approach provides a uniform framework for the study of structured specifications independently from any actual choice of specification building operators, and moreover it unifies the theory and the model oriented approaches. Within this framework we develop concepts and results about ‘abstract structured specifications ’ such as colimits, model amalgamation, compactness, interpolation, sound and complete proof theory, and pushoutstyle parameterization with sharing, all of them in a top down manner dictated by the upper level of institution independence. 1.
May I Borrow Your Logic? (Transporting Logical Structures along Maps)
, 1995
"... It can be very advantageous to borrow key components of a logic for use in another logic. The advantages are both conceptual and practical; due to the existence of software systems supporting mechanized reasoning in a given logic, it may be possible to reuse a system developed for one logicfor ex ..."
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It can be very advantageous to borrow key components of a logic for use in another logic. The advantages are both conceptual and practical; due to the existence of software systems supporting mechanized reasoning in a given logic, it may be possible to reuse a system developed for one logicfor example, a theoremproverto obtain a new system for another. Translations between logics by appropriate mappings provide a first natural way of reusing tools of one logic in another. This paper generalizes this idea to the case where entire componentsfor example, the proof theoryof one of the logics involved may be completely missing, so that the appropriate mapping could not even be defined. The idea then is to borrow the missing components (as well as their associated tools if they exist) from a logic that has them in order to create the fullfledged logic and tools that we desire. The relevant structure is transported using maps that only involve a limited aspect of the two logics ...