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Compiling Dyadic FirstOrder Specifications into Map Algebra
"... Two techniques are designed for eliminating quantifiers from an existentially quantified conjunction of dyadic literals, in terms of the operators... , ∩, and... of the TarskiChinGivant formalism of relations. The use of such techniques is illustrated through increasingly challenging examples, ..."
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Two techniques are designed for eliminating quantifiers from an existentially quantified conjunction of dyadic literals, in terms of the operators... , ∩, and... of the TarskiChinGivant formalism of relations. The use of such techniques is illustrated through increasingly challenging examples, and their algorithmic complexity is assessed.
Threevariable statements of setpairing
 Theoretical Computer Science
"... The approach to algebraic specifications of set theories proposed by Tarski and Givant inspires current research aimed at taking advantage of the purely equational nature of the resulting formulations for enhanced automation of reasoning on aggregates of various kinds: sets, bags, hypersets, etc. Th ..."
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The approach to algebraic specifications of set theories proposed by Tarski and Givant inspires current research aimed at taking advantage of the purely equational nature of the resulting formulations for enhanced automation of reasoning on aggregates of various kinds: sets, bags, hypersets, etc. The viability of the said approach rests upon the possibility to form ordered pairs and to decompose them by means of conjugated projections. Ordered pairs can be conceived of in many ways: along with the most classic one, several other pairing functions are examined, which can be preferred to it when either the axiomatic assumptions are too weak to enable pairing formation à la Kuratowski, or they are strong enough to make the specification of conjugated projections particularly simple, and their formal properties easy to check within the calculus of binary relations.
Compiling Dyadic FirstOrder Specifications into Map Calculus, by Folding Quantifiers into Map Composition
"... Two techniques are designed for eliminating quantiers from an existentially quantied conjunction of dyadic literals, in terms of the operators , \, and 1 of the TarskiChinGivant formalism of relations. The use of such techniques is illustrated through increasingly challenging examples, and their ..."
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Two techniques are designed for eliminating quantiers from an existentially quantied conjunction of dyadic literals, in terms of the operators , \, and 1 of the TarskiChinGivant formalism of relations. The use of such techniques is illustrated through increasingly challenging examples, and their algorithmic complexity is assessed. Key words. Algebraic logic, quantier elimination, computational complexity. It was early discovered that simple algebraic specications, which consist of listings of sort symbols, operation symbols, and equations, are in their pure form not appropriate for writing down specications of larger software systems. Roughly speaking, in this regard they correspond to assembly code and not to structured programs of high level languages. ([EM85], p.3) 1 Introduction In relational DBMSs, both the data denition language and the query language are organized on two levels: SQL (or Datalog) operates at a higher and manoriented level, while relational algebra a...