Composition of Different-Type Relations via the Kleisli Category for the Continuation Monad View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2018-10-06

AUTHORS

Koki Nishizawa , Norihiro Tsumagari

ABSTRACT

We give the way of composing different types of relational notions under certain condition, for example, ordinary binary relations, up-closed multirelations, ordinary (possibly non-up-closed) multirelations, quantale-valued relations, and probabilistic relations. Our key idea is to represent a relational notion as a generalized predicate transformer based on some truth value in some category and to represent it as a Kleisli arrow for some continuation monad. The way of composing those relational notions is given via identity-on-object faithful functors between different Kleisli categories. We give a necessary and sufficient condition to have such identity-on-object faithful functor. More... »

PAGES

97-112

References to SciGraph publications

  • 2010. Convexity, Duality and Effects in THEORETICAL COMPUTER SCIENCE
  • 1971. Categories for the Working Mathematician in NONE
  • 2006. Monotone Predicate Transformers as Up-Closed Multirelations in RELATIONS AND KLEENE ALGEBRA IN COMPUTER SCIENCE
  • 1994-10. Effect algebras and unsharp quantum logics in FOUNDATIONS OF PHYSICS
  • 1998. Refinement Calculus, A Systematic Introduction in NONE
  • 2015. A Relation-Algebraic Approach to Multirelations and Predicate Transformers in MATHEMATICS OF PROGRAM CONSTRUCTION
  • Book

    TITLE

    Relational and Algebraic Methods in Computer Science

    ISBN

    978-3-030-02148-1
    978-3-030-02149-8

    Author Affiliations

    From Grant

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-030-02149-8_7

    DOI

    http://dx.doi.org/10.1007/978-3-030-02149-8_7

    DIMENSIONS

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