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21
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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Cited by 47 (32 self)
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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...
A Presheaf Semantics of ValuePassing Processes
, 1996
"... This paper investigates presheaf models for process calculi with value passing. Denotational semantics in presheaf models are shown to correspond to operational semantics in that bisimulation obtained from open maps is proved to coincide with bisimulation as defined traditionally from the operat ..."
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Cited by 33 (18 self)
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This paper investigates presheaf models for process calculi with value passing. Denotational semantics in presheaf models are shown to correspond to operational semantics in that bisimulation obtained from open maps is proved to coincide with bisimulation as defined traditionally from the operational semantics. Both "early" and "late" semantics are considered, though the more interesting "late" semantics is emphasised. A presheaf model and denotational semantics is proposed for a language allowing process passing, though there remains the problem of relating the notion of bisimulation obtained from open maps to a more traditional definition from the operational semantics.
Geometric logic in computer science
 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 speci cation languages. 1 ..."
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Cited by 13 (3 self)
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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 speci cation languages. 1
Locales Are Not Pointless
 Theory and Formal Methods 1994: Proceedings of the Second Imperial College Department of Computing Workshop on Theory and Formal Methods, Mller
, 1994
"... The KripkeJoyal semantics is used to interpret the fragment of intuitionistic logic containing ; ! and 8 in the category of locales. An axiomatic theory is developed that can be interpreted soundly in two ways, using either lower or upper powerlocales, so that pairs of separate results can be pr ..."
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Cited by 13 (4 self)
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The KripkeJoyal semantics is used to interpret the fragment of intuitionistic logic containing ; ! and 8 in the category of locales. An axiomatic theory is developed that can be interpreted soundly in two ways, using either lower or upper powerlocales, so that pairs of separate results can be proved as single formal theorems. Openness and properness of maps between locales are characterized by descriptions using the logic, and it is proved that a locale is open iff its lower powerlocale has a greatest point. The entire account is constructive and holds for locales over any topos. 1
Query Languages for Bags
 University of Pennsylvania
, 1993
"... In this paper we study theoretical foundations for programming with bags. We fully determine the strength of many polynomial bag operators relative to an ambient query language. Then picking the strongest combination of these operators we obtain the yardstick nested bag query language NBL(monus ; u ..."
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Cited by 7 (5 self)
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In this paper we study theoretical foundations for programming with bags. We fully determine the strength of many polynomial bag operators relative to an ambient query language. Then picking the strongest combination of these operators we obtain the yardstick nested bag query language NBL(monus ; unique). The relationship between nested relational algebra and various fragments of NBL(monus ; unique) is investigated. The precise amount of extra power that NBL(monus ; unique) possesses over the nested relational algebra is determined. An ordering for dealing with partial information in bags is proposed and a technique for lifting a linear order at base types to linear order at all types is presented. This linear order is used to prove the conservative extension property for several bag languages. Using this property, we prove some inexpressibility results for NBL(monus ; unique). In particular, it can not test for a property that is simultaneously infinite and coinfinite (for exampl...
Lower Bag Domains
 FUNDAMENTA INFORMATICAE
, 1995
"... Two lower bag domain constructions are introduced: the initial construction which gives free lower monoids, and the final construction which is defined explicitly in terms of second order functions. The latter is analyzed closely. For sober dcpo's, the elements of the final lower bag domains c ..."
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Cited by 7 (3 self)
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Two lower bag domain constructions are introduced: the initial construction which gives free lower monoids, and the final construction which is defined explicitly in terms of second order functions. The latter is analyzed closely. For sober dcpo's, the elements of the final lower bag domains can be described concretely as bags. For continuous domains, initial and final lower bag domains coincide. They are continuous again and can be described via a basis which is constructed from a basis of the argument domain. The lower bag domain construction preserves algebraicity and the properties I and M, but does not preserve bounded completeness, property L, or bifiniteness.
On Representation and Querying Incomplete Information in Databases with Multisets
, 1995
"... We extend the approach to representation of partial information based on orderings on objects from sets to multisets. We characterize orderings arising under the closed and the openworld assumptions and analyze their complexity. We prove that, in contrast to the set case, where orderings are first ..."
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Cited by 5 (2 self)
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We extend the approach to representation of partial information based on orderings on objects from sets to multisets. We characterize orderings arising under the closed and the openworld assumptions and analyze their complexity. We prove that, in contrast to the set case, where orderings are firstorder definable and are thus expressible in standard database query languages, the orderings on bags are not expressible in standard bag languages. As a corollary of this result, we give an example of a query on nested relations whose inexpressibility in the extension of relational algebra to nested objects cannot be proved by reduction to the firstorder case. 1 Introduction An approach to representation of partial information in databases that treats objects as elements of partially ordered sets, where the meaning of the order is "being more informative," has proved to be very useful for analyzing incompleteness of information in the relational database model and its extensions [3, 5, 8,...
Geometric Logic As A Specification Language
 in: Hankin, Mackie and Nagarajan (eds), Theory and Formal Methods of Computing
"... The "observational content" of geometric logic is discussed and it is proposed that geometric logic is an appropriate basis for a Zlike specification language in which schemas are used as geometric theory presentations. ..."
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Cited by 5 (3 self)
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The "observational content" of geometric logic is discussed and it is proposed that geometric logic is an appropriate basis for a Zlike specification language in which schemas are used as geometric theory presentations.
Fundamentals of object oriented database modelling. Intellektual ~ny Sistemy (Intelligent Systems
 Intelligent Systems
, 1996
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