Revising basic theorem proving algorithms to cope with the logic of partial functions

Partial terms are those that can fail to denote a value; such terms arise frequently in the specification and development of programs. Earlier papers describe and argue for the use of the non-classical "Logic of Partial Functions" (LPF) to facilitate sound and convenient reasoning about such terms. This paper reviews the fundamental theorem proving algorithms -such as resolutionand identifies where they need revision to cope with LPF. Particular care is needed with "refutation" procedures. The modified algorithms are justified with respect to a semantic model. Indications are provided of further work which could lead to efficient support for LPF. © 2014 Newcastle University. Printed and published by Newcastle University, Computing Science, Claremont Tower, Claremont Road, Newcastle upon Tyne, NE1 7RU, England. Bibliographical details JONES, C, B., LOVERT, M, J., STEGGLES, L, J. Revising Basic Theorem Proving Algorithms to Cope with the Logic of Partial Functions [By] C. B. Jones, M. J. Lovert and L. J. Steggles Newcastle upon Tyne: Newcastle University: Computing Science, 2014. (Newcastle University, Computing Science, Technical Report Series, No. CS-TR-1414)