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Handling Inconsistencies in Z Using Quasi-Classical Logic

  • Ralph Miarka
  • John Derrick
  • Eerke Boiten
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2272)

Abstract

The aim of this paper is to discuss what formal support can be given to the process of living with inconsistencies in Z, rather than eradicating them. Logicians have developed a range of logics to continue to reason in the presence of inconsistencies. We present one representative of such paraconsistent logics, namely Hunter’s quasi-classical logic, and apply it to the analysis of inconsistent Zsc hemas. In the presence of inconsistency quasi-classical logic allows us to derive less, but more “useful”, information. Consequently, inconsistent Z specifications can be analysed in more depth than at present. Part of the analysis of a Zoperation is the calculation of the precondition. However, in the presence of an inconsistency, information about the intended application of the operation may be lost. It is our aim to regain this information. We introduce a new classification of precondition areas, based on the notions of definedness, overdefinedness and undefinedness. We then discuss two options to determine these areas both of which are based on restrictions of classical reasoning.

Keywords

Classical Logic Proof Theory Operation Change Paraconsistent Logic Expansion Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ralph Miarka
    • 1
  • John Derrick
    • 1
  • Eerke Boiten
    • 1
  1. 1.Computing LaboratoryUniversity of KentCanterburyUK

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