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13
The UniForM Workbench, a Universal Development Environment for Formal Methods
 FM'99
, 1999
"... The UniForM Workbench supports combination of Formal Methods (on a solid logical foundation), provides tools for the development of hybrid, realtime or reactive systems, transformation, verification, validation and testing. Moreover, it... ..."
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Cited by 20 (2 self)
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The UniForM Workbench supports combination of Formal Methods (on a solid logical foundation), provides tools for the development of hybrid, realtime or reactive systems, transformation, verification, validation and testing. Moreover, it...
Combining and Representing Logical Systems Using ModelTheoretic Parchments
 In Recent Trends in Algebraic Development Techniques, volume 1376 of LNCS
, 1997
"... . The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. We adopt the modeltheoretic view of logic as captured in the notions of institution and of parchment (an algebraic way of presenting institutions). We prop ..."
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Cited by 15 (4 self)
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. The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. We adopt the modeltheoretic view of logic as captured in the notions of institution and of parchment (an algebraic way of presenting institutions). We propose a new, modified notion of parchment together with parchment morphisms and representations. In contrast to the original parchment definition and our earlier work, in modeltheoretic parchments introduced here the universal semantic structure is distributed over individual signatures and models. We lift formal properties of the categories of institutions and their representations to this level: the category of modeltheoretic parchments is complete, and their representations may be put together using categorical limits as well. However, modeltheoretic parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessar...
Categorial Fibring of Logics with Terms and Binding Operators
 FRONTIERS OF COMBINING SYSTEMS 2, STUDIES IN LOGIC AND COMPUTATION
, 1998
"... Categorial characterizations are given of both unconstrained and constrained fibring of Hibert calculi and interpretation systems for languages with variables, terms, variable binding operators and modal like operators. Some preliminary transference results are established. A brief comparison wi ..."
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Cited by 14 (10 self)
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Categorial characterizations are given of both unconstrained and constrained fibring of Hibert calculi and interpretation systems for languages with variables, terms, variable binding operators and modal like operators. Some preliminary transference results are established. A brief comparison with model theoretic parchments is included.
Combining and Representing Logical Systems
, 1997
"... The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. Following Goguen and Burstall, we adopt the modeltheoretic view of logic as captured in the notion of institution and of parchment (a certain algebraic ..."
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Cited by 12 (3 self)
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The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. Following Goguen and Burstall, we adopt the modeltheoretic view of logic as captured in the notion of institution and of parchment (a certain algebraic way of presenting institutions). We propose a modified notion of parchment together with a notion of parchment morphism and representation, respectively. We lift formal properties of the categories of institutions and their representations to this level: the category of parchments is complete, and parchment representations may be put together using categorical limits as well. However, parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessary invention for proper combination of various logical features may be introduced either on an ad hoc basis (when putting parchments together using limits in the cat...
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 ...
Combining Logics: Parchments Revisited
 In Recent Trends in Algebraic Development Techniques, volume 2267 of LNCS
, 2001
"... generalizes the common situation when truthvalues are ordered, we require a whole Tarskian closure operation as in [2]. In the sequel, AlgSig denotes the category of algebraic many sorted signatures with a distinguished sort (for formulae) and morphisms preserving it. Given such a signature hS; ..."
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Cited by 7 (5 self)
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generalizes the common situation when truthvalues are ordered, we require a whole Tarskian closure operation as in [2]. In the sequel, AlgSig denotes the category of algebraic many sorted signatures with a distinguished sort (for formulae) and morphisms preserving it. Given such a signature hS; Oi, we denote by Alg(hS; Oi) the category of hS; Oi algebras, and by cAlg(hS; Oi) the class of all pairs hA; i with A 2 jAlg(hS; Oi)j and a closure operation on A . Denition 1. A layered parchment is a tuple P = hSig; L; Mi where: { Sig is a category (of abstract<F13
Representations, Hierarchies, and Graphs of Institutions
, 1996
"... For the specification of abstract data types, quite a number of logical systems have been developed. In this work, we will try to give an overview over this variety. As a prerequisite, we first study notions of {\em representation} and embedding between logical systems, which are formalized as {\em ..."
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Cited by 5 (4 self)
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For the specification of abstract data types, quite a number of logical systems have been developed. In this work, we will try to give an overview over this variety. As a prerequisite, we first study notions of {\em representation} and embedding between logical systems, which are formalized as {\em institutions} here. Different kinds of representations will lead to a looser or tighter connection of the institutions, with more or less good possibilities of faithfully embedding the semantics and of reusing proof support. In the second part, we then perform a detailed ``empirical'' study of the relations among various wellknown institutions of total, ordersorted and partial algebras and firstorder structures (all with Horn style, i.e.\ universally quantified conditional, axioms). We thus obtain a {\em graph} of institutions, with different kinds of edges according to the different kinds of representations between institutions studied in the first part. We also prove some separation results, leading to a {\em hierarchy} of institutions, which in turn naturally leads to five subgraphs of the above graph of institutions. They correspond to five different levels of expressiveness in the hierarchy, which can be characterized by different kinds of conditional generation principles. We introduce a systematic notation for institutions of total, ordersorted and partial algebras and firstorder structures. The notation closely follows the combination of features that are present in the respective institution. This raises the question whether these combinations of features can be made mathematically precise in some way. In the third part, we therefore study the combination of institutions with the help of socalled parchments (which are certain algebraic presentations of institutions) and parchment morphisms. The present book is a revised version of the author's thesis, where a number of mathematical problems (pointed out by Andrzej Tarlecki) and a number of misuses of the English language (pointed out by Bernd KriegBr\"uckner) have been corrected. Also, the syntax of specifications has been adopted to that of the recently developed Common Algebraic Specification Language {\sc Casl} \cite{CASL/Summary,Mosses97TAPSOFT}.
Cryptomorphisms at Work
 Recent Trends in Algebraic Development Techniques  Selected Papers, volume 3423 of Lecture Notes in Computer Science
, 2005
"... We show that the category proposed in [5] of logic system presentations equipped with cryptomorphisms gives rise to a category of parchments that is both complete and translatable to the category of institutions, improving on previous work [15]. We argue that limits in this category of parchment ..."
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Cited by 4 (2 self)
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We show that the category proposed in [5] of logic system presentations equipped with cryptomorphisms gives rise to a category of parchments that is both complete and translatable to the category of institutions, improving on previous work [15]. We argue that limits in this category of parchments constitute a very powerful mechanism for combining logics.
Completeness Results for Fibred Parchments Beyond the Propositional Base
 Recent Trends in Algebraic Development Techniques  Selected Papers, volume 2755 of Lecture Notes in Computer Science
, 2003
"... In [6] it was shown that fibring could be used to combine institutions presented as cparchments, and several completeness preservation results were established. However, their scope of applicability was limited to propositionalbased logics. Herein, we extend these results to a broader class of ..."
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Cited by 4 (3 self)
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In [6] it was shown that fibring could be used to combine institutions presented as cparchments, and several completeness preservation results were established. However, their scope of applicability was limited to propositionalbased logics. Herein, we extend these results to a broader class of logics, possibly including variables, terms and quantifiers.
Context Parchments
"... . The paper introduces a notion of context parchment. The notion is illustrated by several examples. It is shown, that every logical context parchment generates a context institution. Morphisms between context parchments are introduced, thus yielding a category of context parchments. The use of uni ..."
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Cited by 1 (0 self)
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. The paper introduces a notion of context parchment. The notion is illustrated by several examples. It is shown, that every logical context parchment generates a context institution. Morphisms between context parchments are introduced, thus yielding a category of context parchments. The use of universal constructions in the category of context parchments, for modular construction of logics is discussed and illustrated by examples. 1 Introduction Institutions, were introduced to provide an "abstract model theory for specification and programming"quoting from the title of [8]. The modeltheoretic view of logic, advocated by institutions, seems to be very natural in computer science applications, considering the fact, that our main concern is to specify, create, and reason about concrete objectssuch as programs or VLSI chips. Context institutions (cf. [13]), enrich the structure of institutions by adding notions such as contexts, and substitutions, retaining at the same time the...