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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 ..."
Abstract

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}.
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
Algebraic System Specification and Development: Survey and Annotated Bibliography  Second Edition 
, 1997
"... Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . ..."
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Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.2 Action Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.7 Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.1 Early Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.2 Recent Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . 55 4.7.3 The Common Framework Initiative. . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5 Methodology 57 5.1 Development Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.1 Applica...
Heterogeneous Logical Environments for . . .
"... We use the theory of institutions to capture the concept of a heterogeneous logical environment as a number of institutions linked by institution morphisms and comorphisms. We discuss heterogeneous specifications built in such environments, with interinstitutional specification morphisms based on ..."
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We use the theory of institutions to capture the concept of a heterogeneous logical environment as a number of institutions linked by institution morphisms and comorphisms. We discuss heterogeneous specifications built in such environments, with interinstitutional specification morphisms based on both institution morphisms and comorphisms. We distinguish three kinds of heterogeneity: (1) specifications in logical environments with universal logic (2) heterogeneous specifications focused at a particular logic, and (3) heterogeneous specifications distributed over a number of logics.
Institutional semantics for manyvalued logics
"... We develop manyvalued logic, including a generic abstract model theory, over a fully abstract syntax. We show that important manyvalued logic model theories, such as traditional firstorder manyvalued logic and fuzzy multialgebras, may be conservatively embedded into our abstract framework. Our ..."
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We develop manyvalued logic, including a generic abstract model theory, over a fully abstract syntax. We show that important manyvalued logic model theories, such as traditional firstorder manyvalued logic and fuzzy multialgebras, may be conservatively embedded into our abstract framework. Our development is technically based upon the socalled theory of institutions of Goguen and Burstall and may serve as a template for defining at hand manyvalued logic model theories over various concrete syntaxes or, from another perspective, to combine manyvalued logic with other logical systems. We also show that our generic manyvalued logic abstract model theory enjoys a couple of important institutional model theory properties that support the development of deep model theory methods. Key words: institutions, manyvalued logic 1.