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# Handling Inconsistencies in Z using Quasi-Classical Logic

Miarka, Ralph and Derrick, John and Boiten, Eerke Albert (2002) Handling Inconsistencies in Z using Quasi-Classical Logic. In: Berto, Didier and Bowen, Jonathan P. and Henson, Martin C. and Robinson, Ken, eds. ZB 2002:Formal Specification and Development in Z and B 2nd International Conference of B and Z Users. Lecture Notes in Computer Science . Springer, Berlin, Germany, pp. 204-225. ISBN 978-3-540-43166-4. E-ISBN 978-3-540-45648-3. (doi:10.1007/3-540-45648-1_11) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication) Official URLhttp://dx.doi.org/10.1007/3-540-45648-1_11

## 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 Z schemas. 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 Z operation 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.

Item Type: Book section 10.1007/3-540-45648-1_11 Z, Quasi-classical logic, Inconsistency Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming, Faculties > Sciences > School of Computing > Theoretical Computing Group E. Boiten 24 Nov 2008 18:00 UTC 30 May 2019 11:43 UTC https://kar.kent.ac.uk/id/eprint/13830 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-9184-8968
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