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Algebraic GraphBased Approach to Management of MultiBase Systems,II: Mathematical Aspects of Schema Integration
 TR9502, FRAME INFORM SYSTEMS
, 1995
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Partial Horn logic and cartesian categories
 ANNALS OF PURE AND APPLIED LOGIC 145 (3) (2007), PP. 314 353
, 2009
"... A logic is developed in which function symbols are allowed to represent partial functions. It has the usual rules of logic (in the form of a sequent calculus) except that the substitution rule has to be modified. It is developed here in its minimal form, with equality and conjunction, as partial Hor ..."
Abstract

Cited by 9 (4 self)
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A logic is developed in which function symbols are allowed to represent partial functions. It has the usual rules of logic (in the form of a sequent calculus) except that the substitution rule has to be modified. It is developed here in its minimal form, with equality and conjunction, as partial Horn logic. Various kinds of logical theory are equivalent: partial Horn theories, quasiequational theories (partial Horn theories without predicate symbols), cartesian theories and essentially algebraic theories. The logic is sound and complete with respect to models in Set, and sound with respect to models in any cartesian (finite limit) category. The simplicity of the quasiequational form allows an easy predicative constructive proof of the free partial model theorem for cartesian theories: that if a theory morphism is given from one cartesian theory to another, then the forgetful (reduct) functor from one model category to the other has a left adjoint. Various examples of quasiequational theory are studied, including those of cartesian categories and of other classes of categories. For each quasiequational theory T another, CartϖT, is constructed, whose models are cartesian categories equipped with models of T. Its initial model, the classifying category for T, has properties similar to those of the syntactic category, but more precise with respect to strict cartesian functors.
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...
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"... Managing cognitive aspects of conceptual modeling and design in the arrow diagram logic framework: A mathematician’s view 1 terms suitable for computer processing which will be simultaneously transparent for a human. Thus the problem necessarily contains aspects of both cognitive and formal cognitiv ..."
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Managing cognitive aspects of conceptual modeling and design in the arrow diagram logic framework: A mathematician’s view 1 terms suitable for computer processing which will be simultaneously transparent for a human. Thus the problem necessarily contains aspects of both cognitive and formal cognitive and formal logic. A key point in the CMDproblems is that the universe to be specified is not an example from a textbook but a piece of reality like a bank or an airport. In addition, the specification has to be somehow extracted from multiple, very informal and often hardly consistent descriptions provided by different people. Moreover, as the process of information system design is going on, and mutual understanding between the contributors is increasing, these partial descriptions may be changed so that the entire specification is permanently revised and corrected. On a whole, the design process goes along something like a spiral rather than a direct line, and thus the conceptual model is endlessly reengineered until the approaching deadline captures it as it is. So, a conceptual model has to compress a bulky array of diverse information into a compact comprehensible specification suitable for effective communication between the database designers,
Generalised Sketches as an algebraic graphbased framework for semantic modeling and database design
, 1997
"... A graphbased specification language and the corresponding machinery are described as stating a basic framework for semantic modeling and database design. It is shown that a few challenging theoretical questions in the area, and some of hot practical problems as well, can be successfully approached ..."
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A graphbased specification language and the corresponding machinery are described as stating a basic framework for semantic modeling and database design. It is shown that a few challenging theoretical questions in the area, and some of hot practical problems as well, can be successfully approached in the framework. The machinery has its origin in the classical sketches invented by Ehresmann and is close to their generalization recently proposed by Makkai. There are two essential distinctions from Makkai's sketches. One consists in a different  more direct  formalization of sketches that categorists (and database designers) usually draw. The second distinction is more fundamental and consists in introducing operational sketches specifying complex diagram operations over ordinary (predicate) sketches, correspondingly, models of operational sketches are diagram algebras. Together with the notion of parsing operational sketches, this is the main mathematical contribution of the pape...