Even though it is not very often admitted, partial functions do play a signiicant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a three-valued logic decades ago, but there has not been a satisfactory mechanisation. Based on this, we have developed resolution and tableau calculi for automated theorem proving. The ...

The calculus of relations has been widely used in program specification and reasoning. It is very tempting to use such specifications as running prototypes of the desired program, but, even considering finite domains, the inherent partiality and non-determinism of relations makes this impractical and highly inefficient. To tame partiality we prescribe the usage of invariants, represented by cor...

Even though it is not very often admitted, partial functions do play a signii-cant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a three-valued logic decades ago. This approach allows rejecting certain unwanted formulae as faulty, which the simpler two-valued ones accept. We have developed resolution and tableau ...