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Institution Morphisms
, 2001
"... Institutions formalize the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasizes the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces ..."
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Cited by 57 (17 self)
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Institutions formalize the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasizes the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces terminology to clearly distinguish several levels of generality of the institution concept. A surprising number of different notions of morphism have been suggested for forming categories with institutions as objects, and an amazing variety of names have been proposed for them. One goal of this paper is to suggest a terminology that is uniform and informative to replace the current chaotic nomenclature; another goal is to investigate the properties and interrelations of these notions in a systematic way. Following brief expositions of indexed categories, diagram categories, twisted relations, and Kan extensions, we demonstrate and then exploit the duality between institution morphisms in the original sense of Goguen and Burstall, and the "plain maps" of Meseguer, obtaining simple uniform proofs of completeness and cocompleteness for both resulting categories. Because of this duality, we prefer the name "comorphism" over "plain map;" moreover, we argue that morphisms are more natural than comorphisms in many cases. We also consider "theoroidal" morphisms and comorphisms, which generalize signatures to theories, based on a theoroidal institution construction, finding that the "maps" of Meseguer are theoroidal comorphisms, while theoroidal morphisms are a new concept. We introduce "forward" and "seminatural" morphisms, and develop some of their properties. Appendices discuss institutions for partial algebra, a variant of order sorted algebra, two versions of hidden algebra, and...
Composing Hidden Information Modules over Inclusive Institutions
 In From ObjectOrientation to Formal Methods: Essays in Honor of JohanOle Dahl
, 2003
"... This paper studies the composition of modules that can hide information, over a very general class of logical systems called inclusive institutions. Two semantics are given for composition of such modules using five familiar operations, and a property called conservativity is shown necessary and suf ..."
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Cited by 20 (3 self)
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This paper studies the composition of modules that can hide information, over a very general class of logical systems called inclusive institutions. Two semantics are given for composition of such modules using five familiar operations, and a property called conservativity is shown necessary and sufficient for these semantics to agree. The first semantics extracts the visible properties of the result of composing the visible and hidden parts of modules, while the second uses only the visible properties of the components; the semantics agree when the visible consequences of hidden information are enough to determine the result of the composition. A number of "laws of software composition" are proved relating the composition operations. Inclusive institutions simplify many proofs.
Under consideration for publication in Math. Struct. in Comp. Science Axiomatizability in Inclusive Equational Logic
"... A categorical framework for equational logics is presented, together with axiomatizability results in the style of Birkhoff. The distinctive categorical structures used are inclusion systems, an alternative to factorization systems in which factorization is required to be unique rather than unique “ ..."
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A categorical framework for equational logics is presented, together with axiomatizability results in the style of Birkhoff. The distinctive categorical structures used are inclusion systems, an alternative to factorization systems in which factorization is required to be unique rather than unique “up to an isomorphism”. In this framework, models are any objects, equations are special epimorphisms in C, while satisfaction is injectivity. A first result says that equationsasepimorphisms define exactly the quasivarieties, suggesting that epimorphisms actually represent conditional equations. In fact, it is shown that the projectivity/freeness of the domain of epimorphisms is what makes the difference between unconditional and conditional equations, the first defining the varieties, as expected. An abstract version of the axiom of choice seems to be sufficient for free objects to be projective, in which case the definitional power of equations of projective and free domain, respectively, is the same. Connections with other abstract formulations of equational logics are investigated in the end, together with an organization of our logic as an institution. 1.
Composing Hidden Information Modules over Inclusive Institutions
"... Abstract: This paper studies the composition of modules that canhide information, over a very general class of logical systems called inclusive institutions. Two semantics are given for composition ofsuch modules using five familiar operations, and a property called conservativity is shown necessary ..."
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Abstract: This paper studies the composition of modules that canhide information, over a very general class of logical systems called inclusive institutions. Two semantics are given for composition ofsuch modules using five familiar operations, and a property called conservativity is shown necessary and sufficient for these semanticsto agree. The first semantics extracts the visible properties of the result of composing the visible and hidden parts of modules, whilethe second uses only the visible properties of the components; the semantics agree when the visible consequences of hidden informationare enough to determine the result of the composition. A number of &quot;laws of software composition &quot; are proved relating the compositionoperations. Inclusive institutions simplify many proofs. 1 Introduction Modularization limits the complexity of large systems by composing them fromparts; this eases both initial construction and later modification, and also facilitates reuse. Parameterized programming [10, 11] significantly further enhancesflexibility and reusability, by providing parameterized modules along with views, also called fitting morphisms, which say how to fit the syntax of a formal parameter to an actual parameter in a convenient, flexible way, including defaults when there is only one choice; moreover, views can be parameterized, dependent typesare supported through formal parameters that are parameterized by previously introduced formal parameters, and module expressions compose modules intosystems. The module composition operations in this paper are for aggregating, 1
A Foundational Approach to Modularization (Extended Abstract)
"... This paper introduces the novel concept of inclusive institution as a foundational framework for studying logicindependent module compositionality, defines specification modules as specifications allowing both public and private signatures, and shows that an internal property of modules, called con ..."
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This paper introduces the novel concept of inclusive institution as a foundational framework for studying logicindependent module compositionality, defines specification modules as specifications allowing both public and private signatures, and shows that an internal property of modules, called conservatism, is crucial for compositional semantics.
Composition of Modules with Hidden Information over Inclusive Institutions
"... This paper studies the composition of modules that can hide information, over a very general class of logical systems called inclusive institutions. Two semantics are given for compositions using five familiar operations, and a property called conservativity is shown necessary and sufficient for the ..."
Abstract
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This paper studies the composition of modules that can hide information, over a very general class of logical systems called inclusive institutions. Two semantics are given for compositions using five familiar operations, and a property called conservativity is shown necessary and sufficient for these semantics to agree. The first semantics extracts the visible properties of the result of composing both the visible and hidden parts of modules, while the second uses only the visible properties of the components. Several "laws of software composition" are given, which demonstrate the power of inclusive institutions to simplify proofs.