Traditional (classical) Floyd-Hoare logic is defined for a case of total pre- and postconditions while programs can be partial. In the chapter we propose to extend this logic for partial conditions. To do this we first construct and investigate special program algebras of partial predicates, functions, and programs. In such algebras program correctness assertions are presented with the help of a special composition called Floyd-Hoare composition. This composition is monotone and continuous. Considering the class of constructed algebras as a semantic base we then define an extended logic – Partial Floyd-Hoare Logic – and investigate its properties. This logic has rather complicated soundness constraints for inference rules, therefore simpler sufficient constraints are proposed. The logic constructed can be used for program verification.


Program algebra program logic partial predicate soundness composition-nominative approach 


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Copyright information

© Springer International Publishing 2013

Authors and Affiliations

  • Andrii Kryvolap
    • 1
  • Mykola Nikitchenko
    • 1
  • Wolfgang Schreiner
    • 2
  1. 1.Taras Shevchenko National University of KyivKyivUkraine
  2. 2.Johannes Kepler UniversityLinzAustria

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