Avoiding the Undefined by Underspecification

The first volume of Springer-Verlag's Lecture Notes in Computer Science appeared in 1973, almost 22 years ago. The field has learned a lot about computing since then, and in doing so it has leaned on and supported advances in other fields. In this paper, we discuss an aspect of one of these fields that has been explored by computer scientists, handling undefined terms in formal logic. Logicians are concerned mainly with studying logic n o t using it. Some computer scientists have discovered, by necessity, that logic is actually a useful tool. Their at tempts to use logic have led to new insights -new axiomatizations, new proof formats, new meta-logical notions like relative completeness, and new concerns. We, the authors, are computer scientists whose interests have forced us to become users of formal logic. We use it in our work on language definition and in the formal development of programs. This paper is born of that experience. The operation of a computer is nothing more than uninterpreted symbol manipulation. Bits are moved and altered electronically, without regard for what they denote. It i swe who provide the interpretation, saying that one bit string represents money and another someone's name, or that one transformation represents addition and another alphabetization. Our programs define sequences of uninterpreted symbol manipulations, and we elect to construe these as meaningful transformations on data. How do we justify a belief that a program performs a meaningful transformation -how do we know that it "works"? Few programs produce outputs that are continuous in their inputs, so testing some input-output pairs and generalizing does not work. It is only by deriving, from a program's text, properties satisfied