1 Alan Turing and the development of Artificial Intelligence ∗ Stephen Muggleton , Hilbert at the 1928 International Mathematical Congress. Hilbert presented three open questions During the centennial year of his birth Alan Turing for logic and mathematics. Was mathematics (1912-1954) has been widely celebrated as having laid 1. complete in the sense that any mathematical the foundations for Computer Science, Automated De- assertion could either be proved or disproved, cryption, Systems Biology and the Turing Test. In this 2. consistent in the sense that false statements paper we investigate Turing’s motivations and expec- tations for the development of Machine Intelligence, as could not be derived by a sequence of valid expressed in his 1950 article in Mind. We show that steps and many of the trends and developments within AI over 3. decidable in the sense that there exists a def- the last 50 years were foreseen in this foundational pa- inite method to decide the truth or falsity of per. In particular, Turing not only describes the use every mathematical assertion. of Computational Logic but also the necessity for the development of Machine Learning in order to achieve Within three years Kurt G¨odel [13] had shown human-level AI within a 50 year time-frame. His de- that not even the axoims of arithmetic are both scription of the Child Machine (a machine which learns complete and consistent and by 1937 both Alonzo like an infant) dominates the closing section of the pa- Church [5] and Alan Turing [43] had demonstrated per, in which he provides suggestions for how AI might the undecidability of particular mathematical as- be achieved. Turing discusses three alternative sug- sertions. gestions which can be characterised as: 1) AI by pro- While G¨odel and Church had depended on gramming, 2) AI by ab initio machine learning and 3) demonstrating their results using purely math- AI using logic, probabilities, learning and background ematical calculi, Turing had taken the unusual knowledge. He argues that there are inevitable limi- route of considering mathematical proof as an ar- tations in the first two approaches and recommends tifact of human reasoning. He thus considered a the third as the most promising. We compare Turing’s physical machine which emulated a human math- three alternatives to developments within AI, and con- clude with a discussion of some of the unresolved chal- ematician using a pen and paper together with a lenges he posed within the paper. series of instructions. Turing then generalised this notion to a universal machine which could emu- Keywords: Alan Turing, Artificial Intelligence, Ma- chine Intelligence late all other computing machines. He used this construct to show that certain functions cannot be computed by such a universal machine, and conse- 1. Introduction quently demonstrated the undecidability of asser- tions associated with such functions. In this section we will first review relevant parts At the heart of Turing’s universal machine is of the early work of Alan Turing which pre-dated a model of human calculation. It was this choice his paper in Mind [42]. which set the scene for later discussions on the degree to which computers might be capable of 1.1. Early work: the Entscheidungsproblem more sophisticated human-level reasoning. Turing’s initial investigations of computation stemmed from the programme set out by David 1.2. Bletchley Park *Corresponding author: Stephen Muggleton, Department The outbreak of the Second World War provided of Computing, Imperial College London. Turing with an opportunity and resources to de- AI Communications ISSN 0921-7126, IOS Press. All rights reserved 2 S. Muggleton / Turing and the development of AI sign and test a machine which would emulate hu- the building of machines designed to carry out man reasoning. Acting as the UK’s main wartime this or that complicated task. He was now fas- decryption centre, Bletchley Park had recruited cinated with the idea of a machine that could many of the UK’s best mathematicians in an at- learn. tempt to decode German military messages. By 1940 the Bombe machine, designed by Turing and Welchman [7], had gone into operation and was ef- 2. Turing’s 1950 paper in Mind ficiently decrypting messages using methods pre- viously employed manually by human decoders. In keeping with Turing’s background in Mathemati- 2.1. Structure of the paper cal Logic, the Bombe design worked according to a reductio ad absurdum principle which simplified The opening sentence of Turing’s 1950 paper the hypothesis space of 263 possible settings for the [42] declares Enigma machine to a small number of possibilities I propose to consider the question, “Can ma- based on a given set of message transcriptions. chines think?” The hypothesis elimination principle of the Bombe was later refined in the design of the Colos- The first six sections of the paper provide a philo- sus I and II machines. The Tunny report [15] (de- sophical framework for answering this question. classified by the UK government in 2000), shows These sections are briefly summarised below. that one of the key technical refinements of Colos- sus was the use of Bayesian reasoning to order the 1. The Imitation Game. Often referred to as search through the space of hypothetical settings the “Turing test”, this is a form of parlour for the Lorenz encryption machine. This combi- game involving a human interrogator who al- nation of logical hypothesis generation tied with ternately questions a hidden computer and a Bayesian evaluation were later to become central hidden person in an attempt to distinguish to approaches used within Machine Learning (see the identity of the respondents. The Imita- Section 5). Indeed strong parallels exist between tion Game is aimed at providing an objective decryption tasks on the one hand, which involve test for deciding whether machines can think. hypothesising machine settings from a set of mes- 2. Critique of the New Problem. Turing dis- sage transcriptions and modern Machine Learning cusses the advantages of the game for the pur- tasks on the other hand, which involve hypothesis- poses of deciding whether machines and hu- ing a model from a set of observations. Given their mans could be attributed with thinking on grounding in the Bletchley Park decryption work an equal basis using objective human judge- it is hardly surprising that two of the authors of ment. the Tunny report, Donald Michie (1923-2007) and 3. The Machines Concerned in the Game. Tur- Jack Good (1916-2009), went on to play founding ing indicates that he intends digital comput- roles in the post-war development of Machine In- ers to be the only kind of machine permitted telligence and Subjective Probabilistic reasoning to take part in the game. respectively. In numerous out-of-hours meetings at 4. Digital Computers. The nature of the new Bletchley Park, Turing discussed the problem of digital computers, such as the Manchester machine intelligence with both Michie and Good. machine, is explained and compared to Charles According to Andrew Hodges [16], Turing’s biog- Babbage’s proposals for an Analytical En- rapher gine. These meetings were an opportunity for Alan 5. Universality of Digital Computers. Turing to develop the ideas for chess-playing machines explains how digital computers can emulate that had begun in his 1941 discussions with any discrete-state machine. Jack Good. They often talked about mechani- 6. Contrary Views on the Main Question. Nine sation of thought processes, bringing in the the- traditional philosophical objections to the ory of probability and weight of evidence, with proposition that machines can think are in- which Donald Michie was by now familiar. troduced and summarily dismissed by Tur- He (Turing) was not so much concerned with ing. S. Muggleton / Turing and the development of AI 3 2.2. Learning machines - Section 7 of Turing would be a very practicable possibility even by paper present techniques. It is probably not necessary to increase the speed of operations of the ma- The task of engineering software which ad- chines at all. Parts of modern machines which dresses the central question of Turing’s paper have can be regarded as analogs of nerve cells work dominated Artificial Intelligence research over the about a thousand times faster than the lat- last sixty years. In the final section of the 1950 ter. This should provide a “margin of safety” paper Turing addresses the motivation and possi- which could cover losses of speed arising in ble approaches for such endeavours. His transition many ways. Our problem then is to find out from the purely philosophical nature of the first how to programme these machines to play the six sections of the paper is marked as follows. game. At my present rate of working I produce The only really satisfactory support that can about a thousand digits of programme a day, be given for the view expressed at the begin- so that about sixty workers, working steadily ning of section 6, will be that provided by wait- through the fifty years might accomplish the ing for the end of the century and then doing job, if nothing went into the wastepaper bas- the experiment described. But what can we say ket. Some more expeditious method seems de- in the meantime? sirable. Turing goes on to discuss three distinct strategies In retrospect it is amazing that Turing managed to which might be considered capable of achieving a foresee that “Advances in engineering” would lead thinking machine. These can be characterised as to computers with a Gigabyte of storage by the follows: 1) AI by programming, 2) AI by ab initio end of the twentieth century. It is also noteworthy machine learning and 3) AI using logic, probabil- that Turing suggests that in terms of hardware, it ities, learning and background knowledge.