A History of Satisfiability

Abstract

This chapter traces the links between the notion of Satisfiability and the attempts by mathematicians, philosophers, engineers, and scientists over the last 2300 years to develop effective processes for emulating human reasoning and scientific discovery, and for assisting in the development of electronic computers and other electronic components. Satisfiability was present implicitly in the development of ancient logics such as Aristotle’s syllogistic logic, its extentions by the Stoics, and Lull’s diagrammatic logic of the medieval period. From the renaissance to Boole algebraic approaches to effective process replaced the logics of the ancients and all but enunciated the meaning of Satisfiability for propositional logic. Clarification of the concept is credited to Tarski in working out necessary and sufficient conditions for “p is true” for any formula p in first-order syntax. At about the same time, the study of effective process increased in importance with the resulting development of lambda calculus, recursive function theory, and Turing machines, all of which became the foundations of computer science and are linked to the notion of Satisfiability. Shannon provided the link to the computer age and Davis and Putnam directly linked Satisfiability to automated reasoning via an algorithm which is the backbone of most modern SAT solvers. These events propelled the study of Satisfiability for the next several decades, reaching “epidemic proportions” in the 1990s and 2000s, and the chapter concludes with a brief history of each of the major Satisfiability-related research tracks that developed during that period.