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17
Algebraic GraphBased Approach to Management of MultiBase Systems,II: Mathematical Aspects of Schema Integration
 TR9502, FRAME INFORM SYSTEMS
, 1995
"... ..."
Databases as Graphical Algebras: Algebraic GraphBased Approach to Data Modeling and Database Design
, 1996
"... . The approach we suggest is based on a graphical specification language possessing formal semantics so that graphical images themselves are precise specifications suitable for implementation. Our specifications are similar to the sketches developed in the category theory but, in contrast to them, ..."
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Cited by 8 (5 self)
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. The approach we suggest is based on a graphical specification language possessing formal semantics so that graphical images themselves are precise specifications suitable for implementation. Our specifications are similar to the sketches developed in the category theory but, in contrast to them, enjoy the possibility of setting arbitrary signatures of diagram properties and operations. An important (and sometimes crucial) step in the process of database design is schema (or view) integration, that is, an activity aimed at producing a global conceptual schema of a database from a set of locally developed useroriented schemas (views). In our approach, correspondence between semantic schemas to be integrated is specified by equations so that the integration procedure can be reduced to algebraic manipulations with sketches representing schemas. This provides the possibility of automated view integration and, correspondingly, automated database design. In the paper the mathemat...
Graphbased logic and sketches I: The general framework. Available by web browser from http://www.cwru.edu/1/class/mans/math/pub/wells
, 1996
"... Sketches as a method of specification of mathematical structures are an alternative to the stringbased specification employed in mathematical logic. ..."
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Sketches as a method of specification of mathematical structures are an alternative to the stringbased specification employed in mathematical logic.
Complexity Doctrines
, 1995
"... vii Introduction ix 1 Tensor and Linear Time 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.1 Almost Equational Specification : : : : : : : : : : : : : : : : : 3 1.1.1 Sketches : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.1.2 Orthogonality : : : : : : : : : : ..."
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vii Introduction ix 1 Tensor and Linear Time 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.1 Almost Equational Specification : : : : : : : : : : : : : : : : : 3 1.1.1 Sketches : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.1.2 Orthogonality : : : : : : : : : : : : : : : : : : : : : : : 5 1.1.3 Essentially Algebraic Specification : : : : : : : : : : : : 8 1.2 Tensor and System T : : : : : : : : : : : : : : : : : : : : : : : 10 1.2.1 Serial Composition : : : : : : : : : : : : : : : : : : : : 10 1.2.2 Parallel Composition : : : : : : : : : : : : : : : : : : : 11 1.2.3 Unary Numbers : : : : : : : : : : : : : : : : : : : : : : 13 1.2.4 System T : : : : : : : : : : : : : : : : : : : : : : : : : 13 1.3 Comprehensions and Tiers : : : : : : : : : : : : : : : : : : : : 15 1.3.1 Comprehensions : : : : : : : : : : : : : : : : : : : : : : 15 1.3.2 Extents : : : : : : : : : : : : : : : : : : : : : : : : : : 18 1.3.3 Dyadic Numbers : : : : : : : : : : : : : : : ...
First Order Logic with Dependent Sorts, with Applications to Category Theory. Book manuscript
, 1995
"... §1. Logic with dependent sorts p. 14 §2. Formal systems p. 32 §3. Quantificational fibrations p. 39 ..."
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§1. Logic with dependent sorts p. 14 §2. Formal systems p. 32 §3. Quantificational fibrations p. 39
Proving Semantical Equivalence of Data Specifications
 J. Pure and Applied Algebra
, 2005
"... More than two decades ago, Peter Freyd introduced essentially algebraic specifications, a wellbehaved generalization of algebraic specifications, allowing for equational partiality. These essentially algebraic specifications turn out to have a number of very interesting applications in computer ..."
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More than two decades ago, Peter Freyd introduced essentially algebraic specifications, a wellbehaved generalization of algebraic specifications, allowing for equational partiality. These essentially algebraic specifications turn out to have a number of very interesting applications in computer science.
A parameterization process as a categorical construction
, 908
"... Abstract. The parameterization process used in the symbolic computation systems Kenzo and EAT is studied here as a general construction in a categorical framework. This parameterization process starts from a given specification and builds a parameterized specification by transforming some operations ..."
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Abstract. The parameterization process used in the symbolic computation systems Kenzo and EAT is studied here as a general construction in a categorical framework. This parameterization process starts from a given specification and builds a parameterized specification by transforming some operations into parameterized operations, which depend on one additional variable called the parameter. Given a model of the parameterized specification, each interpretation of the parameter, called an argument, provides a model of the given specification. Moreover, under some relevant terminality assumption, this correspondence between the arguments and the models of the given specification is a bijection. It is proved in this paper that the parameterization process is provided by a free functor and the subsequent parameter passing process by a natural transformation. Various categorical notions are used, mainly adjoint functors, pushouts and lax colimits. 1
CATEGORICAL DATASPECIFICATIONS
, 1995
"... We introduce MDsketches, which are a particular kind of Finite Sum sketches. Two interesting results about MDsketches are proved. First, we show that, given two MDsketches, it is algorithmically decidable whether their model categories are equivalent. Next we show that dataspecifications, as use ..."
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We introduce MDsketches, which are a particular kind of Finite Sum sketches. Two interesting results about MDsketches are proved. First, we show that, given two MDsketches, it is algorithmically decidable whether their model categories are equivalent. Next we show that dataspecifications, as used in databasedesign and software engineering, can be translated to MDsketches. As a corollary, we obtain that equivalence of dataspecifications is decidable.
Diagrammatic Inference
, 710
"... Abstract. Diagrammatic logics were introduced in 2002, with emphasis on the notions of specifications and models. In this paper we improve the description of the inference process, which is seen as a Yoneda functor on a bicategory of fractions. A diagrammatic logic is defined from a morphism of limi ..."
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Abstract. Diagrammatic logics were introduced in 2002, with emphasis on the notions of specifications and models. In this paper we improve the description of the inference process, which is seen as a Yoneda functor on a bicategory of fractions. A diagrammatic logic is defined from a morphism of limit sketches (called a propagator) which gives rise to an adjunction, which in turn determines a bicategory of fractions. The propagator, the adjunction and the bicategory provide respectively the syntax, the models and the inference process for the logic. Then diagrammatic logics and their morphisms are applied to the semantics of side effects in computer languages.