A semantic analysis of logics that cope with partial terms

Authors:
Cliff B. Jones;Matthew J. Lovert;L. Jason Steggles
Affiliations:
School of Computing Science, Newcastle University, UK;School of Computing Science, Newcastle University, UK;School of Computing Science, Newcastle University, UK
Venue:
ABZ'12 Proceedings of the Third international conference on Abstract State Machines, Alloy, B, VDM, and Z
Year:
2012

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Abstract

Specifications of programs frequently involve operators and functions that are not defined over all of their (syntactic) domains. Proofs about specifications ---and those to discharge proof obligations that arise in justifying steps of design--- must be based on formal rules. Since classical logic deals only with defined values, some extra thought is required. There are several ways of handling terms that can fail to denote a value -- this paper provides a semantically based comparison of three of the best known approaches. In addition, some pointers are given to further alternatives.