3 Sixty Years of Stable Models David Pearce 3.1 Introduction This paper relates some episodes in the history of logic from the mid-twentieth Century to a highly influential line of research in logic programming and artificial intelligence that developed independently from around the end of the 1980s. 1 In 1988 Michael Gelfond and Vladimir Lifschitz published a celebrated paper (1988) on the stable model semantics of logic programs. Today, having built on and enlarged those key ideas of 24 years ago, answer set programming (often abbrevi- ated as ASP) has emerged over the last decade as a flourishing paradigm of declarative programming, rich in theoretical advances and maturing applications. 2 This is one aspect of the legacy of stable models, and a very important one. Another aspect, equally important, but somewhat farther from the limelight today, lies in the ability of stable models to provide us with a valuable method of reasoning – to give it a name let us call it stable reasoning. In this essay I examine some of the foundational concepts underlying the approach of stable models. I try to answer the question: “What is a stable model?” by searching for a purely logical grasp of the stability concept. In so doing, I shall discuss some concepts and results in logic from more than 60 years ago. In particular, I look at questions such as: • How does a notion of stability presented in a work on intuitionistic mathematics in 1947 relate to the Gelfond-Lifschitz concept of 1988? • How does the notion of constructible falsity published in 1949 help to explain properties of negation arising in the language of ASP? • Why is a seminal paper by McKinsey and Tarski (1948) important for understanding the relations between answer sets and modal and 73 K. Mulligan et al. (eds.), The History and Philosophy of Polish Logic © Palgrave Macmillan, a division of Macmillan Publishers Limited 2014