Fork Algebras in Algebra, Logic and Computer Science

Frias, Marcelo F.; Baum, Gabriel; Haeberer, Armando Martin

doi:10.3233/fi-1997-32101

Cited by 21 publications

(3 citation statements)

References 27 publications

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“…10], in [34, §3] the formalisation of the proof calculus for ω-closure fork algebras with urelements [35,Def. 7] (a variant of fork algebras [36,37] with a reflexive and transitive closure operator) requires the use of strict monoidal categories [29, Ch. VII, §1] whose monoid of objects is given by the (not necessarily finite) subsets of the corresponding class of equations.…”

Section: Definition 28 (Proof Calculus [2])mentioning

confidence: 99%

“…Many examples of this relation between logics have been developed, one of the most prominent examples being the translation from modal logic to first-order logic with equality [60]. Many other examples are worth mentioning, such as algebraisations of different logics, like those relating fork algebras [61,62], an extension of relation algebras [63,64], with several other logics (c.f. [37,65]).…”

Section: Relating Satisfiability Calculimentioning

confidence: 99%

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Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems

Pombo

Castro

Aguirre

et al. 2019

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The theory of institutions, introduced by Goguen and Burstall in 1984, can be thought of as an abstract formulation of model theory. This theory has been shown to be particularly useful in computer science, as a mathematical foundation for formal approaches to software construction. Institution theory was extended by a number of researchers, José Meseguer among them, who, in 1989, presented General Logics, wherein the model theoretical view of institutions

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Section: Definition 28 (Proof Calculus [2])mentioning

confidence: 99%

Section: Relating Satisfiability Calculimentioning

confidence: 99%

Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems

Pombo

Castro

Aguirre

et al. 2019

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“…See details and proof in(Oliveira, 2011). 13 It is termed split in(Bird and de Moor, 1997) and fork in(Frias et al, 1997). 14 This parallel between attribute sets ordered by inclusion and projection functions ordered by injectivity is dealt with in detail in(Oliveira, 2011).…”

mentioning

confidence: 99%

A relation-algebraic approach to the “Hoare logic” of functional dependencies

Oliveira¹

2014

Journal of Logical and Algebraic Methods in Programming

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Inspired by the trend on unifying theories of programming, this paper shows how the algebraic treatment of standard data dependency theory equips relational data with functional types and an associated type system which is useful for type checking database operations and for query optimization.Such a typed approach to database programming is then shown to be of the same family as other programming logics such as eg. Hoare logic or that of strongest invariant functions which has been used in the analysis of while statements.The prospect of using automated deduction systems such as Prover9 for type-checking and query optimization on top of such an algebraic approach is considered.

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