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Semantic Representations And Query Languages For OrSets
 IN PROCEEDINGS OF 12TH ACM SYMPOSIUM ON PRINCIPLES OF DATABASE SYSTEMS
, 1993
"... Orsets were introduced by Imielinski, Naqvi and Vadaparty for dealing with limited forms of disjunctive information in database queries. Independently, Rounds used a similar notion for representing disjunctive and conjunctive information in the context of situation theory. In this paper we formulat ..."
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Cited by 41 (21 self)
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Orsets were introduced by Imielinski, Naqvi and Vadaparty for dealing with limited forms of disjunctive information in database queries. Independently, Rounds used a similar notion for representing disjunctive and conjunctive information in the context of situation theory. In this paper we formulate a query language with adequate expressive power for orsets. Using the notion of normalization of orsets, queries at the "structural" and "conceptual" levels are distinguished. Losslessness of normalization is established for a large class of queries. We have obtained upper bounds for the cost of normalization. An approach related to that of Rounds is used to provide semantics for orsets. We also treat orsets in the context of partial information in databases.
Information Systems for Continuous Posets
, 1993
"... The method of information systems is extended from algebraic posets to continuous posets by taking a set of tokens with an ordering that is transitive and interpolative but not necessarily reflexive. This develops results of Raney on completely distributive lattices and of Hoofman on continuous S ..."
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Cited by 17 (4 self)
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The method of information systems is extended from algebraic posets to continuous posets by taking a set of tokens with an ordering that is transitive and interpolative but not necessarily reflexive. This develops results of Raney on completely distributive lattices and of Hoofman on continuous Scott domains, and also generalizes Smyth's "Rstructures". Various constructions on continuous posets have neat descriptions in terms of these continuous information systems; here we describe HoffmannLawson duality (which could not be done easily with Rstructures) and Vietoris power locales. 2 We also use the method to give a partial answer to a question of Johnstone's: in the context of continuous posets, Vietoris algebras are the same as localic semilattices.
An Elementary Proof That Upper and Lower Powerdomain Constructions Commute
 BULLETIN OF THE EATCS
, 1992
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An Upper Power Domain Construction in terms of Strongly Compact Sets
 MFPS '91. LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... A novel upper power domain construction is defined by means of strongly compact sets. Its power domains contain less elements than the classical ones in terms of compact sets, but still admit all necessary operations, i.e. they contain less junk. The notion of strong compactness allows a proof of st ..."
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Cited by 4 (3 self)
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A novel upper power domain construction is defined by means of strongly compact sets. Its power domains contain less elements than the classical ones in terms of compact sets, but still admit all necessary operations, i.e. they contain less junk. The notion of strong compactness allows a proof of stronger properties than compactness would, e.g. an intrinsic universal property of the upper power construction, and its commutation with the lower construction.
Algebraic Characterization of Edible Powerdomains
, 1993
"... Powerdomains like mixes, sandwiches, snacks and scones are typically used to provide semantics of collections of descriptions of partial data. In particular, they were used to give semantics of databases with partial information. In this paper we argue that to be able to put these constructions into ..."
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Cited by 2 (2 self)
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Powerdomains like mixes, sandwiches, snacks and scones are typically used to provide semantics of collections of descriptions of partial data. In particular, they were used to give semantics of databases with partial information. In this paper we argue that to be able to put these constructions into the context of a programming language it is necessary to characterize them as free (ordered) algebras. Two characterizations  for mixes and snacks  are already known, and in the first part of the paper we give characterizations for scones and sandwiches and provide an alternative characterization of snacks. The algebras involved have binary and unary operations and relatively simple equational theories. We then define a new construction, which is in essence all others put together (hence called salad) and give its algebraic characterization. It is also shown how all algebras considered in the paper are related in a natural way, that is, in a way that corresponds to embeddings of their p...
Comment.Math.Univ.Carolin. 50,2 (2009) 297–314 297 Lattices of Scottclosed sets
"... Abstract. A dcpo P is continuous if and only if the lattice C(P) of all Scottclosed subsets of P is completely distributive. However, in the case where P is a noncontinuous dcpo, little is known about the order structure of C(P). In this paper, we study the ordertheoretic properties of C(P) for g ..."
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Abstract. A dcpo P is continuous if and only if the lattice C(P) of all Scottclosed subsets of P is completely distributive. However, in the case where P is a noncontinuous dcpo, little is known about the order structure of C(P). In this paper, we study the ordertheoretic properties of C(P) for general dcpo’s P. The main results are: (i) every C(P) is Ccontinuous; (ii) a complete lattice L is isomorphic to C(P) for a complete semilattice P if and only if L is weakstably Calgebraic; (iii) for any two complete semilattices P and Q, P and Q are isomorphic if and only if C(P) and C(Q) are isomorphic. In addition, we extend the function P 7 → C(P) to a left adjoint functor from the category DCPO of
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"... Injective locales over perfect embeddings and algebras of the upper powerlocale monad ..."
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Injective locales over perfect embeddings and algebras of the upper powerlocale monad