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A Categorical Logic for Information Systems
 Journal of the Interest Group in Pure and Applied Logic
, 1996
"... Category theoretic models of information systems have by now been widely used in industrial consultancies (for some examples see [6] and [3]) and the models themselves have been developed in some detail in, for example, [4], [1], [10], [5], [11], [2] and [8]. Although many information systems are n ..."
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Category theoretic models of information systems have by now been widely used in industrial consultancies (for some examples see [6] and [3]) and the models themselves have been developed in some detail in, for example, [4], [1], [10], [5], [11], [2] and [8]. Although many information systems are never meant to be implemented computationally (for example paperbased enterprise wide information models are frequently used by senior executives to help understand and plan the development of large corporations), the logic of an information system corresponds to the logic of the query language that might be used for interrogating the system (whether or not it is implemented). Typically this logic corresponds to a variation of predicate logic applied to simple finite domains. Most categorical information system modellers either avoid being explicit about the logic of their systems (thus acquiring the logic of whatever query language happens to be present in an implementation) or import the ...
Semantics of Binary Choice Constructs
"... This paper is a summary of the following six publications: (1) Stable Power Domains [Hec94d] (2) Product Operations in Strong Monads [Hec93b] (3) Power Domains Supporting Recursion and Failure [Hec92] (4) Lower Bag Domains [Hec94a] (5) Probabilistic Domains [Hec94b] (6) Probabilistic Power Domains, ..."
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This paper is a summary of the following six publications: (1) Stable Power Domains [Hec94d] (2) Product Operations in Strong Monads [Hec93b] (3) Power Domains Supporting Recursion and Failure [Hec92] (4) Lower Bag Domains [Hec94a] (5) Probabilistic Domains [Hec94b] (6) Probabilistic Power Domains, Information Systems, and Locales [Hec94c] After a general introduction in Section 0, the main results of these six publications are summarized in Sections 1 through 6. 0 Introduction In this section, we provide a common framework for the summarized papers. In Subsection 0.1, Moggi's approach to specify denotational semantics by means of strong monads is introduced. In Subsection 0.2, we specialize this approach to languages with a binary choice construct. Strong monads can be obtained in at least two ways: as free constructions w.r.t. algebraic theories (Subsection 0.3), and by using second order functions (Subsection 0.4). Finally, formal definitions of those concepts which are used in all...
Some Properties of Query Languages for Bags
 In Proceedings of 4th International Workshop on Database Programming Languages
, 1993
"... In this paper we study the expressive power of query languages for nested bags. We define the ambient bag language by generalizing the constructs of the relational language of BreazuTannen, Buneman and Wong, which is known to have precisely the power of the nested relational algebra. Relative s ..."
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In this paper we study the expressive power of query languages for nested bags. We define the ambient bag language by generalizing the constructs of the relational language of BreazuTannen, Buneman and Wong, which is known to have precisely the power of the nested relational algebra. Relative strength of additional polynomial constructs is studied, and the ambient language endowed with the strongest combination of those constructs is chosen as a candidate for the basic bag language, which is called BQL (Bag Query Language). We prove that achieveing the power of BQL in the relational language amounts to adding simple arithmetic to the latter. We show that BQL has shortcomings of the relational algebra: it can not express recursive queries. In particular, parity test is not definable in BQL. We consider augmenting BQL with powerbag and structural recursion to overcome this deficiency. In contrast to the relational case, where powerset and structural recursion are equivalent...
Geometric Logic in Computer Science
 Ryan (Eds.): Theory and Formal Methods
, 1993
"... We present an introduction to geometric logic and the mathematical structures associated with it, such as categorical logic and toposes. We also describe some of its applications in computer science including its potential as a logic for specification languages. ..."
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We present an introduction to geometric logic and the mathematical structures associated with it, such as categorical logic and toposes. We also describe some of its applications in computer science including its potential as a logic for specification languages.
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"... Preface to the TAC reprint This is a reprint of the final version, published by the Centre de Recherche Mathématique at the Université de Montréal. We are aware of only one error, which will be corrected below. If any others are reported, we will post corrections at ftp.math.mcgill.ca/barr/pdffiles/ ..."
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Preface to the TAC reprint This is a reprint of the final version, published by the Centre de Recherche Mathématique at the Université de Montréal. We are aware of only one error, which will be corrected below. If any others are reported, we will post corrections at ftp.math.mcgill.ca/barr/pdffiles/ctcserr. pdf and at