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Relational Complexity and Higher Order Logics

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Foundations of Information and Knowledge Systems (FoIKS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9616))

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Abstract

Relational machines (RM) were introduced as abstract machines that compute queries to relational database instances (dbi’s), that are generic (i.e., that preserve isomorphisms). As RM’s cannot discern between tuples that are equivalent in first order logic with k variables, Relational Complexity was introduced as a complexity theory where the input dbi to a query is measured as its \(\textit{size}_k\), i.e., as the number of classes in the equivalence relation of equality of \(\mathrm {FO}^k\) types of k-tuples in the dbi. We describe the basic notions of Relational Complexity, and survey known characterizations of some of its main classes through different fixed point logics and through fragments of second and third order logics.

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Notes

  1. 1.

    In the sense of [12] these relations are redundant relations.

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Authors and Affiliations

  1. Depto. de Ingeniería e Investigaciones Tecnológicas, Universidad Nacional de La Matanza, Buenos Aires, Argentina

    José Maria Turull-Torres

  2. Massey University, Palmerston North, New Zealand

    José Maria Turull-Torres

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  1. José Maria Turull-Torres
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Correspondence to José Maria Turull-Torres .

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Editors and Affiliations

  1. Faculteit Wetenschappen, Universiteit Hasselt, Hasselt, Belgium

    Marc Gyssens

  2. Dept. Ciencias Ingeniería Computación, Universidad Nacional del Sur, Bahía Blanca, Argentina

    Guillermo Simari

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Turull-Torres, J.M. (2016). Relational Complexity and Higher Order Logics. In: Gyssens, M., Simari, G. (eds) Foundations of Information and Knowledge Systems. FoIKS 2016. Lecture Notes in Computer Science(), vol 9616. Springer, Cham. https://doi.org/10.1007/978-3-319-30024-5_17

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  • DOI: https://doi.org/10.1007/978-3-319-30024-5_17

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