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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
NonTruthFunctional Fibred Semantics
, 2001
"... wing the ideas in [4], to cope with possible non{truth{functionality of constructors. In the spirit of the theory of institutions and general logics [8, 9], we consider a logic to consist of an indexing functor to a suitable category of logic systems. In our case, the logic systems of interest are n ..."
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Cited by 7 (4 self)
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wing the ideas in [4], to cope with possible non{truth{functionality of constructors. In the spirit of the theory of institutions and general logics [8, 9], we consider a logic to consist of an indexing functor to a suitable category of logic systems. In our case, the logic systems of interest are non{truth{functional (ntf) rooms . For simplicity, we shall only work at this level of abstraction. As shown in [3], everything can be smoothly lifted to the fully edged indexed case. In the sequel, AlgSig' denotes the category of algebraic many sorted signatures with a distinguished sort ' (for formulae) and morphisms preserving it. Given one such signature , we denote by Alg() the category of {algebras and {algebra homomorphisms, and by cAlg() the class of all pairs hA; i with A a<
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}.
Categorybased Modularisation for Equational Logic Programming
 Acta Informatica
, 1996
"... : Although modularisation is basic to modern computing, it has been little studied for logicbased programming. We treat modularisation for equational logic programming using the institution of categorybased equational logic in three different ways: (1) to provide a generic satisfaction conditio ..."
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Cited by 5 (5 self)
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: Although modularisation is basic to modern computing, it has been little studied for logicbased programming. We treat modularisation for equational logic programming using the institution of categorybased equational logic in three different ways: (1) to provide a generic satisfaction condition for equational logics; (2) to give a categorybased semantics for queries and their solutions; and (3) as an abstract definition of compilation from one (equational) logic programming language to another. Regarding (2), we study soundness and completeness for equational logic programming queries and their solutions. This can be understood as ordinary soundness and completeness in a suitable "nonlogical" institution. Soundness holds for all module imports, but completeness only holds for conservative module imports. Categorybased equational signatures are seen as modules, and morphisms of such signatures as module imports. Regarding (3), completeness corresponds to compiler correc...
Quantum institutions
 Algebra, Meaning, and Computation – Essays Dedicated to Joseph A. Goguen on the Occasion of His 65th Birthday, volume 4060 of Lecture Notes in Computer Science
, 2006
"... The exogenous approach to enriching any given base logic for probabilistic and quantum reasoning is brought into the realm of institutions. The theory of institutions helps in capturing the precise relationships between the logics that are obtained, and, furthermore, helps in analyzing some of the k ..."
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Cited by 5 (4 self)
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The exogenous approach to enriching any given base logic for probabilistic and quantum reasoning is brought into the realm of institutions. The theory of institutions helps in capturing the precise relationships between the logics that are obtained, and, furthermore, helps in analyzing some of the key design decisions and opens the way to make the approach more useful and, at the same time, more abstract. 1
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.
Structural Properties of Some Categories of Institutions
, 1996
"... : This is a technical paper stating and proving completeness and cocompleteness results for various categories of institutions. 1 Introduction This is a technical companion report to [Tar96], where an overview of various notions of a mapping between institutions is given and some structural propert ..."
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Cited by 3 (1 self)
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: This is a technical paper stating and proving completeness and cocompleteness results for various categories of institutions. 1 Introduction This is a technical companion report to [Tar96], where an overview of various notions of a mapping between institutions is given and some structural properties of the resulting categories of institutions are indicated. The main goal of the current report is to provide technical statements of these results and to prove them in sufficient detail. Some of the results given here have been only hinted at in [Tar96], some of them are repeated from [Tar96], and some are known from the earlier literature. For the sake of completeness of this report we recall all the formal definitions which underly the results  we refrain however from giving any motivations and informal analysis of the role of the notions introduced and results proved. We will also sketch the proofs of known results, since they provide a necessary background for the proofs which hav...