Behind the Scenes of K&CK

Abstract

I was honored to receive the 2009 Dijkstra Prize, joint with Joe Halpern. The circumstances under which the prize was awarded did not allow for more than a brief response. I have since wondered what I might have said in a longer address. I concluded that, rather than discuss the future of the field, I would try to tell the story behind the award-winning paper. This note is a draft of this story, from my very biased and subjective point of view. It is presented here in the style of an added clip in a new DVD of an old movie providing footage of some behind the scenes developments, bloopers etc. In contrast to my other papers, the KC it does not set out to improve, extend, or refine pre-existing work. This is why I think that tracing its origins is of interest. The story of how it came to be touches on some of the issues and topics covered in the paper. Moreover, the published versions of the paper do not properly acknowledge some of the people who have influenced our work on the paper. Perhaps this note can compensate. As a PhD student at Stanford, I attended a series of lectures on logics of programs given by Joe Halpern, who had just moved west to IBM Almaden Research Center, following his post-doc at MIT. I was looking for an advisor, and Joe was likewise seeking a first graduate student. We agreed to try working together toward my PhD, and decided to start by considering logics of knowledge and belief. We knew, based on the work of Kripke and Hintikka in the late Fifties and early Sixties, that these logics are technically similar to the Temporal and Dynamic logics that Joe had been involved with. One new element in our approach was going to be the study of logics with many “knowers,” whereas most of the classical treatment of knowledge and belief focused on the epistemics of a single agent. In a logic for many knowers one could make (and make sense of) statements about what one agent, say Alice, knows about the world and about what another agent (Bob) may know, or be ignorant of. Indeed, knowledge could be further nested, and statements could involve any number of agents. We started looking at the literature on modal logics of programs trying to see how they may apply to logics of knowledge. We also considered other logical issues such as characterizing ignorance by way of what it might mean for an agent to “know only” some set of facts and nothing more. I spent the summer of 1983 doing a student internship at IBM Almaden, working with Joe. Danny Dolev was there, and heard that we were working on logics of knowledge. He told us about a talk he had attended by Robert Aumann at the Hebrew University, who described the “cheating wives” puzzle, and explained that Common Knowledge played an important role. (Roughly at the same time, Joe’s colleague at IBM Shel