A Tableau Calculus for Partial Functions ?

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 mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional logics. However, strong Kleene logic, where quantiication is restricted and therefore not truth-functional, does not t the framework directly. We solve this problem by applying recent methods from sorted logics. This paper presents a tableau calculus that combines the proper treatment of partial functions with the eeciency of sorted calculi.