Results 1 
3 of
3
Goals and benchmarks for automated map reasoning
 Journal of Symbolic Computation
, 2000
"... TarskiGivant’s map calculus is briefly reviewed, and a plan of research is outlined aimed at investigating applications of this ground equational formalism in the theoremproving field. The main goal is to create synergy between firstorder predicate calculus and the map calculus. Techniques for tr ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
TarskiGivant’s map calculus is briefly reviewed, and a plan of research is outlined aimed at investigating applications of this ground equational formalism in the theoremproving field. The main goal is to create synergy between firstorder predicate calculus and the map calculus. Techniques for translating isolated sentences, as well as entire theories, from firstorder logic into map calculus are designed, or in some cases simply brought nearer through the exercise of specifying properties of a few familiar structures (natural numbers, nested lists, finite sets, lattices). It is also highlighted to what extent a stateoftheart theoremprover for firstorder logic, namely Otter, can be exploited not only to emulate, but also to reason about, map calculus. Issues regarding ’safe ’ forms of map reasoning are singled out, in sight of possible generalizations to the database area. 1
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, ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
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.
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 ..."
Abstract
 Add to MetaCart
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...