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24
Equations and rewrite rules: a survey
 In Formal Language Theory: Perspectives and Open Problems
, 1980
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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 41 (6 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.
Modular proof systems for partial functions with Evans equality
 Information and Computation
, 2006
"... The paper presents a modular superposition calculus for the combination of firstorder theories involving both total and partial functions. The modularity of the calculus is a consequence of the fact that all the inferences are pure – only involving clauses over the alphabet of either one, but not bo ..."
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Cited by 25 (13 self)
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The paper presents a modular superposition calculus for the combination of firstorder theories involving both total and partial functions. The modularity of the calculus is a consequence of the fact that all the inferences are pure – only involving clauses over the alphabet of either one, but not both, of the theories – when refuting goals represented by sets of pure formulae. The calculus is shown to be complete provided that functions that are not in the intersection of the component signatures are declared as partial. This result also means that if the unsatisfiability of a goal modulo the combined theory does not depend on the totality of the functions in the extensions, the inconsistency will be effectively found. Moreover, we consider a constraint superposition calculus for the case of hierarchical theories and show that it has a related modularity property. Finally we identify cases where the partial models can always be made total so that modular superposition is also complete with respect to the standard (total function) semantics of the theories. 1
Relating Semantic and ProofTheoretic Concepts for Polynomial Time Decidability of Uniform Word Problems
 In Proceedings 16th IEEE Symposium on Logic in Computer Science, LICS'2001
, 2001
"... In this paper we compare three approaches to polynomial time decidability for uniform word problems for quasivarieties. Two of the approaches, by Evans and Burris, respectively, are semantical, referring to certain embeddability and axiomatizability properties. The third approach is more prooftheor ..."
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Cited by 22 (2 self)
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In this paper we compare three approaches to polynomial time decidability for uniform word problems for quasivarieties. Two of the approaches, by Evans and Burris, respectively, are semantical, referring to certain embeddability and axiomatizability properties. The third approach is more prooftheoretic in nature, inspired by McAllester's concept of local inference. We define two closely related notions of locality for equational Horn theories and show that both the criteria by Evans and Burris lie in between these two concepts. In particular, the variant we call stable locality will be shown to subsume both Evans' and Burris' method.
Hierarchical and modular reasoning in complex theories: The case of local theory extensions
 In Proc. 6th Int. Symp. Frontiers of Combining Systems (FroCos 2007), LNCS 4720
, 2007
"... Abstract. We present an overview of results on hierarchical and modular reasoning in complex theories. We show that for a special type of extensions of a base theory, which we call local, hierarchic reasoning is possible (i.e. proof tasks in the extension can be hierarchically reduced to proof tasks ..."
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Cited by 12 (8 self)
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Abstract. We present an overview of results on hierarchical and modular reasoning in complex theories. We show that for a special type of extensions of a base theory, which we call local, hierarchic reasoning is possible (i.e. proof tasks in the extension can be hierarchically reduced to proof tasks w.r.t. the base theory). Many theories important for computer science or mathematics fall into this class (typical examples are theories of data structures, theories of free or monotone functions, but also functions occurring in mathematical analysis). In fact, it is often necessary to consider complex extensions, in which various types of functions or data structures need to be taken into account at the same time. We show how such local theory extensions can be identified and under which conditions locality is preserved when combining theories, and we investigate possibilities of efficient modular reasoning in such theory combinations. We present several examples of application domains where local theories and local theory extensions occur in a natural way. We show, in particular, that various phenomena analyzed in the verification literature can be explained in a unified way using the notion of locality. 1
Some connections between residual finiteness, finite embeddability and the word problem
 Journal of London Mathematics Society
, 1969
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Finitely Presented Lattices: Canonical Forms And The Covering Relation
 TRANS. AMER. MATH. SOC
, 1989
"... A canonical form for elements of a lattice freely generated by a partial lattice is given. This form agrees with Whitman's canonical form for free lattices when the partial lattice is an antichain. The connection between this canonical form and the arithmetic of the lattice is given. For exa ..."
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Cited by 10 (4 self)
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A canonical form for elements of a lattice freely generated by a partial lattice is given. This form agrees with Whitman's canonical form for free lattices when the partial lattice is an antichain. The connection between this canonical form and the arithmetic of the lattice is given. For example, it is shown that every element of a finitely presented lattice has only finitely many minimal join representations and that every join representation can be refined to one of these. An algorithm is given which decides if a given element of a finitely presented lattice has a cover and finds them if it does. An example is given of a nontrivial, finitely presented lattice with no cover at all.
Some improvements of a lemma of Rosenfeld
, 1996
"... We give some improvements of a lemma of Rosenfeld which permit us to optimize some algorithms in differential algebra: we prove the lemma with weaker hypotheses and we demonstrate an analogue of Buchberger's second criterion, which avoids non necessary reductions for detecting coherent sets of ..."
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Cited by 6 (0 self)
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We give some improvements of a lemma of Rosenfeld which permit us to optimize some algorithms in differential algebra: we prove the lemma with weaker hypotheses and we demonstrate an analogue of Buchberger's second criterion, which avoids non necessary reductions for detecting coherent sets of differential polynomials. We try also to clarify the relations between the theorems in differential algebra and some more widely known results in the Grobner bases theory. Keywords. Differential algebra. Rewrite systems. Buchberger 's criteria. Polynomial differential equations. Rosenfeld 's lemma. 1 Introduction Stated in 1959 by Rosenfeld [Ro59, lemma, page 397], the lemma we improve in this paper can be viewed as a manifestation in differential algebra 1 of the famous KnuthBendix theorem [Ev51] [KB67] in term algebras 2 : Theorem 1 A noetherian rewrite system is locally confluent if and only if it is confluent over its critical pairs. Proof. See [KB67]. 2 Manifestations of theorem ...