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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 ..."
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Cited by 5 (4 self)
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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 examp ..."
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Cited by 3 (3 self)
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Two techniques are designed for eliminating quantifiers from an existentially quantified conjunction of dyadic literals, in terms of the operators... , &cap;, and... of the TarskiChinGivant formalism of relations. The use of such techniques is illustrated through increasingly challenging examples, and their algorithmic complexity is assessed.
Plan of Activities on the Map Calculus
 PROCEEDINGS OF THE AGP98 JOINT CONFERENCE ON DECLARATIVE PROGRAMMING
, 1998
"... TarskiGivant's map calculus is briefly reviewed and a plan of research is outlined, aimed at investigating applications of this formalism in the theoremproving field. The connections between firstorder logic and the map calculus are investigated, focusing on techniques for translating single ..."
Abstract

Cited by 3 (3 self)
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TarskiGivant's map calculus is briefly reviewed and a plan of research is outlined, aimed at investigating applications of this formalism in the theoremproving field. The connections between firstorder logic and the map calculus are investigated, focusing on techniques for translating single sentences from one context to the other as well as on the translation of entire set theories. Issues regarding 'safe' forms of map reasoning are singled out, in sight of possible generalizations to the database area.
Compiling Dyadic FirstOrder Specications into Map Algebra
"... Two techniques are designed for eliminating quanti ers from an existentially quanti ed conjunction of dyadic literals, in terms of the operators , \, and of the TarskiChinGivant formalism of relations. ..."
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Two techniques are designed for eliminating quanti ers from an existentially quanti ed conjunction of dyadic literals, in terms of the operators , \, and of the TarskiChinGivant formalism of relations.
Benchmark #1 for Equational Set Theory
"... Ongoing theoremproving activity is illustrated, which aims at deriving from a weak algebraic specication of set membership lemmas stating that two specic map expressions characterize conjugated projections. This is an essential step before one can instruct a fair experimental comparison (based on O ..."
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Ongoing theoremproving activity is illustrated, which aims at deriving from a weak algebraic specication of set membership lemmas stating that two specic map expressions characterize conjugated projections. This is an essential step before one can instruct a fair experimental comparison (based on Otter, in our case) between formalizations of set theory within full rstorder predicate calculus on the one hand, and within equational map calculus on the other. Key words. Firstorder automated reasoning, map calculus, algebraic logic, set theories.
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...