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39
Probabilistic data exchange
 In Proc. ICDT
, 2010
"... The work reported here lays the foundations of data exchange in the presence of probabilistic data. This requires rethinking the very basic concepts of traditional data exchange, such as solution, universal solution, and the certain answers of target queries. We develop a framework for data exchange ..."
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Cited by 30 (5 self)
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The work reported here lays the foundations of data exchange in the presence of probabilistic data. This requires rethinking the very basic concepts of traditional data exchange, such as solution, universal solution, and the certain answers of target queries. We develop a framework for data exchange over probabilistic databases, and make a case for its coherence and robustness. This framework applies to arbitrary schema mappings, and finite or countably infinite probability spaces on the source and target instances. After establishing this framework and formulating the key concepts, we study the application of the framework to a concrete and practical setting where probabilistic databases are compactly encoded by means of annotations formulated over random Boolean variables. In this setting, we study the problems of testing for the existence of solutions and universal solutions, materializing such solutions, and evaluating target queries (for unions of conjunctive queries) in both the exact sense and the approximate sense. For each of the problems, we carry out a complexity analysis based on properties of the annotation, in various classes of dependencies. Finally, we show that the framework and results easily and completely generalize to allow not only the data, but also the schema mapping itself to be probabilistic.
On The Algebraic Models Of Lambda Calculus
 Theoretical Computer Science
, 1997
"... . The variety (equational class) of lambda abstraction algebras was introduced to algebraize the untyped lambda calculus in the same way Boolean algebras algebraize the classical propositional calculus. The equational theory of lambda abstraction algebras is intended as an alternative to combinatory ..."
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Cited by 21 (11 self)
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. The variety (equational class) of lambda abstraction algebras was introduced to algebraize the untyped lambda calculus in the same way Boolean algebras algebraize the classical propositional calculus. The equational theory of lambda abstraction algebras is intended as an alternative to combinatory logic in this regard since it is a firstorder algebraic description of lambda calculus, which allows to keep the lambda notation and hence all the functional intuitions. In this paper we show that the lattice of the subvarieties of lambda abstraction algebras is isomorphic to the lattice of lambda theories of the lambda calculus; for every variety of lambda abstraction algebras there exists exactly one lambda theory whose term algebra generates the variety. For example, the variety generated by the term algebra of the minimal lambda theory is the variety of all lambda abstraction algebras. This result is applied to obtain a generalization of the genericity lemma of finitary lambda calculus...
A Continuum of Theories of Lambda Calculus Without Semantics
 16TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS 2001), IEEE COMPUTER
, 2001
"... In this paper we give a topological proof of the following result: There exist 2 @0 lambda theories of the untyped lambda calculus without a model in any semantics based on Scott's view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this resul ..."
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Cited by 18 (13 self)
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In this paper we give a topological proof of the following result: There exist 2 @0 lambda theories of the untyped lambda calculus without a model in any semantics based on Scott's view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this result, we positively solve the conjecture, stated by BastoneroGouy [6, 7] and by Berline [10], that the strongly stable semantics is incomplete. 1
Collapsing Partial Combinatory Algebras
 HigherOrder Algebra, Logic, and Term Rewriting
, 1996
"... Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or recursion theory. In this paper we develop some general theory concerning homomorphic images (or collapses) of pca's, obtained by identification of elements in a pc ..."
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Cited by 15 (2 self)
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Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or recursion theory. In this paper we develop some general theory concerning homomorphic images (or collapses) of pca's, obtained by identification of elements in a pca. We establish several facts concerning final collapses (maximal identification of elements). `En passant' we find another example of a pca that cannot be extended to a total one. 1
Additive Structure of Multiplicative Subgroups of Fields and Galois Theory
 DOCUMENTA MATH.
, 2004
"... One of the fundamental questions in current field theory, related to Grothendieck’s conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classificati ..."
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Cited by 6 (4 self)
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One of the fundamental questions in current field theory, related to Grothendieck’s conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classification of additive properties of multiplicative subgroups of fields containing all squares, using pro2Galois groups of nilpotency class at most 2, and of exponent at most 4. This work extends some powerful methods and techniques from formally real fields to general fields of characteristic not 2.
Algebraic Terminological Representation
, 1991
"... This thesis investigates terminological representation languages, as used in klonetype knowledge representation systems, from an algebraic point of view. Terminological representation languages are based on two primitive syntactic types, called concepts and roles, which are usually interpreted mo ..."
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Cited by 5 (1 self)
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This thesis investigates terminological representation languages, as used in klonetype knowledge representation systems, from an algebraic point of view. Terminological representation languages are based on two primitive syntactic types, called concepts and roles, which are usually interpreted modeltheoretically as sets and relations, respectively. I propose an algebraic rather than a modeltheoretic approach. I show that terminological representations can be naturally accommodated in equational algebras of sets interacting with relations, and I use equational logic as a vehicle for reasoning about concepts interacting with roles.
Clones in topology and algebra
 Acta Math. Univ. Comenianae
, 1997
"... Abstract. Clones of continuous maps of topological spaces and clones of homomorphisms of universal algebras are investigated and their initial segments compared. We show, for instance, that for every triple 2 ≤ n1 ≤ n2 ≤ n3 of integers there exist algebras A1 and A2 with two unary operations such th ..."
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Cited by 5 (4 self)
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Abstract. Clones of continuous maps of topological spaces and clones of homomorphisms of universal algebras are investigated and their initial segments compared. We show, for instance, that for every triple 2 ≤ n1 ≤ n2 ≤ n3 of integers there exist algebras A1 and A2 with two unary operations such that the initial ksegments of their clones of homomorphisms are equal exactly when k ≤ n1, isomorphic exactly when k ≤ n2 and elementarily equivalent exactly when k ≤ n3. 1. Concepts and Results 1.1. According to [5], a clone Clo(X) on a nonvoid set X is a collection of finitary operations Xn − → X with n ∈ ω (where ω denotes the set of all finite ordinals), con: Xn − → X with i ∈ n = {0,..., n − 1}, that taining all Cartesian projections p (n) i (x0,..., xn−1) = xi, and closed under all operations Cn m with m, n ∈ ω (called compositions in [5]), defined for every mtuple f0,..., fm−1: Xn − → X of elements of Clo(X) and any g: Xm − → X in Clo(X) with the result f: Xn − → X given by is, maps p (n) i f(x0,..., xn−1) = g(f0(x0,..., xn−1),..., fm−1(x0,..., xn−1)). It is often convenient to regard Clo(X) also as a category k whose objects are all finite powers X 0, X, X 2,... of X, the set of kmorphisms Xn − → X consists of all nary operations of Clo(X) including all projections p (n) i, the set of kmorphisms Xn − → Xm consists of all maps f = f0 ˙ × · · · ˙×fm−1 where (f0,..., fm−1) is an mtuple of nary operations in Clo(X) and f is defined by
P.: Optimal Mal’tsev conditions for congruence modular varieties. Algebra Universalis 53
, 2005
"... Abstract. For varieties, congruence modularity is equivalent to the tolerance intersection property, TIP in short. Based on TIP, it was proved in [5] that for an arbitrary lattice identity implying modularity (or at least congruence modularity) there exists a Mal’tsev condition such that the identit ..."
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Cited by 4 (2 self)
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Abstract. For varieties, congruence modularity is equivalent to the tolerance intersection property, TIP in short. Based on TIP, it was proved in [5] that for an arbitrary lattice identity implying modularity (or at least congruence modularity) there exists a Mal’tsev condition such that the identity holds in congruence lattices of algebras of a variety if and only if the variety satisfies the corresponding Mal’tsev condition. However, the Mal’tsev condition constructed in [5] is not the simplest known one in general. Now we improve this result by constructing the best Mal’tsev condition and various related conditions. As an application, we give a particularly easy new proof of Freese and Jónsson [11] stating that modular congruence varieties are Arguesian, and we strengthen this result by replacing ”Arguesian ” by ”higher Arguesian ” in the sense of Haiman [18]. We show that lattice terms for congruences of an arbitrary congruence modular variety can be computed in two steps: the first step mimics the use of congruence distributivity while the second step corresponds to congruence permutability. Particular cases of this result were known; the present approach using TIP is even simpler than the proofs of the previous partial results. 1.
Representing congruence lattices of lattices with partial unary operations as congruence lattices of lattices. I. Interval equivalence
, 2002
"... Let L be a bounded lattice, let [a, b] and [c, d] be intervals of L, and let ϕ: [a, b] → [c, d] be an isomorphism between these two intervals. Let us considerthe algebra L ↔ = 〈L; ∧, ∨,ϕ,ϕ ϕ −1 〉, which is a lattice with two partial unary operations. We construct a bounded lattice K (in fact, a c ..."
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Cited by 3 (1 self)
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Let L be a bounded lattice, let [a, b] and [c, d] be intervals of L, and let ϕ: [a, b] → [c, d] be an isomorphism between these two intervals. Let us considerthe algebra L ↔ = 〈L; ∧, ∨,ϕ,ϕ ϕ −1 〉, which is a lattice with two partial unary operations. We construct a bounded lattice K (in fact, a convex extension of L) such that the congruence lattice of L ↔ is isomorphic ϕ to the congruence lattice of K, and extend this result to (many) families of isomorphisms. This result presents a lattice K whose congruence lattice is derived from the congruence lattice of L in a novel way.