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DomainIndependent Queries on Databases with External Functions
 in "LNCS 893: Proceedings of 5th International Conference on Database Theory," 177190
, 1995
"... We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with f ..."
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Cited by 13 (2 self)
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We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with fixpoints or other kinds of iterators. Next, we define two new notions of computable queries with external functions, and prove that they are equivalent, under the assumption that the external functions are total. Thus, our definition of computable queries with external functions is robust. Finally, based on the equivalence result, we give examples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines are complete for complex objects: it was known that they are not complete over flat relations. 1 Introduction Database functionalities are important both for practical and for theoretical purposes. E.g. the system O 2 of ...
Single Identities for Lattice Theory and for Weakly Associative Lattices
 Algebra Universalis
, 1995
"... . We present a single identity for the variety of all lattices that is much simpler than those previously known to us. We also show that the variety of weakly associative lattices is onebased, and we present a generalized onebased theorem for subvarieties of weakly associative lattices that can be ..."
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Cited by 11 (10 self)
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. We present a single identity for the variety of all lattices that is much simpler than those previously known to us. We also show that the variety of weakly associative lattices is onebased, and we present a generalized onebased theorem for subvarieties of weakly associative lattices that can be defined with absorption laws. The automated theoremproving program Otter was used in a substantial way to obtain the results. 1 Introduction Equational identities are, perhaps, the simplest form of sentences expressing many basic properties of algebras. Several familiar classes of algebras, such as semigroups, groups, rings, lattices, and Boolean algebras, are defined by equational identities. Such a class of algebras is known as an equational Supported by the Office of Scientific Computing, U.S. Department of Energy, under Contract W31109Eng38. y Supported by an operating grant from NSERC of Canada (#A8215). class of algebras or a variety of algebras (for mathematical properti...
An Example of Interactive Hardware Transformation
, 1993
"... This article presents an example of correct circuit design through interactive transformation. Interactive transformation differs from traditional hardware design transformation frameworks in that it focuses on the issue of finding suitable hardware architecture for the specified system and the issu ..."
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Cited by 10 (1 self)
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This article presents an example of correct circuit design through interactive transformation. Interactive transformation differs from traditional hardware design transformation frameworks in that it focuses on the issue of finding suitable hardware architecture for the specified system and the issue of architecture correctness. The transformation framework divides every transformation in designs into two steps. The first step is to find a proper architecture implementation. Although the framework does not guarantee existence of such an implementation, nor its discovery, it does provide a characterization of architectural implementation so that the question "is this a correct implementation?" can be answered by equational rewriting. The framework allows a correct architecture implementation to be automatically incorporated with control descriptions to obtain a new system description. The significance of this transformation framework lies in the fact that it requires simpler mechanism o...
Mathematical fuzzy logic as a tool for the treatment of vague information
 Information Sciences
, 2005
"... The paper considers some of the main trends of the recent development of mathematical fuzzy logic as an important tool in the toolbox of approximate reasoning techniques. Particularly the focus is on fuzzy logics as systems of formal logic constituted by a formalized language, by a semantics, and by ..."
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Cited by 10 (1 self)
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The paper considers some of the main trends of the recent development of mathematical fuzzy logic as an important tool in the toolbox of approximate reasoning techniques. Particularly the focus is on fuzzy logics as systems of formal logic constituted by a formalized language, by a semantics, and by a calculus for the derivation of formulas. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon these theoretical considerations. Key words: mathematical fuzzy logic, algebraic semantics, continuous tnorms, leftcontinuous tnorms, Pavelkastyle fuzzy logic, fuzzy set theory, nonmonotonic fuzzy reasoning 1
Nonmodularity Results for Lambda Calculus
 Fundamenta Informaticae
, 2001
"... The variety (equational class) of lambda abstraction algebras was introduced to algebraize the untyped lambda calculus in the same way cylindric and polyadic algebras algebraize the firstorder predicate logic. In this paper we prove that the lattice of lambda theories is not modular and that the va ..."
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Cited by 10 (7 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 cylindric and polyadic algebras algebraize the firstorder predicate logic. In this paper we prove that the lattice of lambda theories is not modular and that the variety generated by the term algebra of a semisensible lambda theory is not congruence modular. Another result of the paper is that the Mal'cev condition for congruence modularity is inconsistent with the lambda theory generated by equating all the unsolvable lambdaterms.
Single Identities for Ternary Boolean Algebras
 Computers and Mathematics with Applications
, 1993
"... this paper, we show that the equational theory of TBAs is onebased. Our methods for finding a single identity for the theory of TBAs are interesting from two distinct points of view. First, from the algebraic, since TBAs enjoy both permutable and distributive congruences, they admit a single ternar ..."
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Cited by 9 (6 self)
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this paper, we show that the equational theory of TBAs is onebased. Our methods for finding a single identity for the theory of TBAs are interesting from two distinct points of view. First, from the algebraic, since TBAs enjoy both permutable and distributive congruences, they admit a single ternary polynomial p(x; y; z), the socalled Pixley polynomial [1, p. 405]. We first find such a polynomial p(x; y; z) and use a technique of R. Padmanabhan and R. W. Quackenbush [7] to construct a single identity for the equational theory in question. This is done in Section 2. Second, from the viewpoint of automated reasoning, we use the program Otter to discover new single identities based upon the results of the algebraic view. Actually we obtain here three new identities shorter in length than those obtained by the formal algebraic process of Section 2each characterizing the equational theory of TBAs. The relevant Otter proofs are also included. 2 The Algebraic View
Partial fields and matroid representation
 Adv. Appl. Math
, 1996
"... A partial field P is an algebraic structure that behaves very much like a field except that addition is a partial binary operation, that is, for some a; b 2 P, a + b may not be defined. We develop a theory of matroid representation over partial fields. It is shown that many important classes of matr ..."
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Cited by 9 (5 self)
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A partial field P is an algebraic structure that behaves very much like a field except that addition is a partial binary operation, that is, for some a; b 2 P, a + b may not be defined. We develop a theory of matroid representation over partial fields. It is shown that many important classes of matroids arise as the class of matroids representable over a partial field. The matroids representable over a partial field are closed under standard matroid operations such as the taking of minors, duals, direct sums and 2sums. Homomorphisms of partial fields are defined. It is shown that if ' : P 1! P 2 is a nontrivial partial field homomorphism, then every matroid representable over P 1 is representable over P 2. The connection with Dowling group geometries is examined. It is shown that if G is a nite abelian group, and r> 2, then there exists a partial field over which the rank{r Dowling group geometry is representable if and only if G has at most one element of order 2, that is, if G is a group in which the identity has at most two square roots.
Recursive Adaptable Grammars
 Master’s Thesis, Worchester Polytechnic Institute
, 1998
"... ContextFree Grammars (CFGs) are a simple and intuitively appealing formalism for the description of programming languages, but lack the computational power to describe many common language features. Over the past three decades, numerous extensions of the CFG model have been developed. Most of these ..."
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Cited by 9 (2 self)
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ContextFree Grammars (CFGs) are a simple and intuitively appealing formalism for the description of programming languages, but lack the computational power to describe many common language features. Over the past three decades, numerous extensions of the CFG model have been developed. Most of these extensions retain a CFG kernel, and augment it with a distinct facility with greater computational power. However, in all the most powerful CFG extensions, the clarity of the CFG kernel is undermined by the opacity of the more powerful extending facility. An intuitively appealing strategy for CFG extension is grammar adaptability, the principle that declarations in a program effectively modify the contextfree grammar of the programming language. An adaptable grammar is equipped with some formal means for modifying its own CFG kernel. Most previous adaptable grammar formalisms have, unfortunately, failed to realize the potential clarity of this concept. In this thesis, a representative samp...
Combination Problems for Commutative/Monoidal Theories or How Algebra Can Help in Equational Unification
 J. Applicable Algebra in Engineering, Communication and Computing
, 1996
"... We study the class of theories for which solving unification problems is equivalent to solving systems of linear equations over a semiring. It encompasses important examples like the theories of Abelian monoids, idempotent Abelian monoids, and Abelian groups. This class has been introduced by the au ..."
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Cited by 7 (7 self)
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We study the class of theories for which solving unification problems is equivalent to solving systems of linear equations over a semiring. It encompasses important examples like the theories of Abelian monoids, idempotent Abelian monoids, and Abelian groups. This class has been introduced by the authors independently of each other as "commutative theories " (Baader) and "monoidal theories" (Nutt). We show that commutative theories and monoidal theories indeed define the same class (modulo a translation of the signature), and we prove that it is undecidable whether a given theory belongs to it. In the remainder of the paper we investigate combinations of commutative/monoidal theories with other theories. We show that finitary commutative/monoidal theories always satisfy the requirements for applying general methods developed for the combination of unification algorithms for disjoint equational theories. Then we study the adjunction of monoids of homomorphisms to commutative /monoidal t...
Undecidable properties of finite sets of equations
 J. Symbolic Logic
, 1976
"... JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JS ..."
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Cited by 6 (2 self)
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JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Association for Symbolic Logic is collaborating with JSTOR to digitize, preserve and extend access to The