A Finite Axiomatization for Fork Algebras

Frias, Marcelo F.; Haeberer, Armando Martin; Veloso, Paulo A. S.

doi:10.1093/jigpal/5.3.1

Cited by 16 publications

(11 citation statements)

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“…But there's also growing interest in QRAs (under various names) in computer science [3,20] and even in automated theorem proving [2].…”

Section: Introductionmentioning

confidence: 99%

Connections between quasi-projective relation algebras and cylindric algebras

Simon¹

2007

Algebra univers.

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In this paper we show that every quasi-projective relation algebra (QRA) has within it cylindric algebras (CAs) of all finite dimensions greater than two such that (i) they are term-definable in the QRA, (ii) they have a relation algebraic reduct that is isomorphic to the QRA and (iii) these isomorphisms are also term-definable. Furthermore, these CAs form a sequence such that each of them is isomorphic to a neat reduct of the higher dimensional ones, and these isomorphisms are also term-definable.These observations yield a new proof of the representation theorem of QRAs, due to Tarski, that is fundamentally different from both his original proof and Maddux's, who generalized Tarski's theorem to a much wider class of algebras.

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“…But there's also growing interest in QRAs (under various names) in computer science [3,20] and even in automated theorem proving [2].…”

Section: Introductionmentioning

confidence: 99%

Connections between quasi-projective relation algebras and cylindric algebras

Simon¹

2007

Algebra univers.

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“…Proper PDOCFA satisfy the axioms [4], and therefore belong to this class. It could be the case that there are models for the axioms that are not proper PDOCFA.…”

Section: A Complete Calculus For Point-dense Omega Closure Fork Agebrasmentioning

confidence: 99%

“…It could be the case that there are models for the axioms that are not proper PDOCFA. Fortunately, the following theorem (which follows from [4] Constraining Quantifiers to Atoms. Alloy quantifiers range over relations of the form { a }, i.e., over unary singletons.…”

Section: A Complete Calculus For Point-dense Omega Closure Fork Agebrasmentioning

confidence: 99%

Alloy Analyzer+PVS in the Analysis and Verification of Alloy Specifications

Frias

Pombo

Moscato

2007

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. This article contains two main contributions. On the theoretical side, it presents a novel complete proof calculus for Alloy. On the applied side we present Dynamite, a tool that combines the semiautomatic theorem prover PVS with the Alloy Analyzer. Dynamite allows one to prove an Alloy assertion from an Alloy specification using PVS, while using the Alloy Analyzer for the automated analysis of hypotheses introduced during the proof process. As a means to assess the usability of the tool, we present a complex case-study based on Zave's Alloy model of addressing for interoperating networks.

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“…Broome and Lipton, 1994;Grädel et al, 1997a;Grädel et al, 1997b), there is nowadays a new burst of interest in the map calculus, stirred up by the publication of Tarski and Givant (1987); in parallel, a big amount of effort is being devoted to the contiguous field of relation algebras (see, e.g. Schmidt and Ströhlein, 1985;Orlowska, 1994;Düntsch, 1997;Frias et al, 1997). This motivates us in proposing here a few directions for research on this formalism, which is fully equational and devoid of individual variables, aimed at bringing to light its practical value for formal computer-based verification.…”

Section: Introductionmentioning

confidence: 99%

Goals and Benchmarks for Automated Map Reasoning

Formisano

Omodeo

Temperini

2000

Journal of Symbolic Computation

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Tarski-Givant's map calculus is briefly reviewed, and a plan of research is outlined aimed at investigating applications of this ground equational formalism in the theorem-proving field. The main goal is to create synergy between first-order predicate calculus and the map calculus. Techniques for translating isolated sentences, as well as entire theories, from first-order 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 stateof-the-art theorem-prover for first-order 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.

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A Finite Axiomatization for Fork Algebras

Cited by 16 publications

References 0 publications

Connections between quasi-projective relation algebras and cylindric algebras

Connections between quasi-projective relation algebras and cylindric algebras

Alloy Analyzer+PVS in the Analysis and Verification of Alloy Specifications

Goals and Benchmarks for Automated Map Reasoning

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