Solution of the Mastermind with an Unlimited Number of Lies as a First Step to Detective Reasoning Modelling

When the author started his career in 1986 his main research interests were Artificial Intelligence(AI), Expert Systems and Decision Support Systems based on AI tools. The first experiment we did was the development of the Anti-Mind and Master Mind with Feedback programs written in the Basic language with an Apple II with 48k of RAM and a 1MHz clock [1]. The Anti-Mind program simulated a good player of the Master Mind game, discovering the secret code defined by the human operator (a sequence of numbers in a pre-defined interval) very quickly. Then we used the algorithm of Anti-Mind to help and correct a human operator trying to discover the secret code defined by the computer resulting in the Master Mind with Feedback. Recently we revisited this work and developed the solution of the Mastermind with an unlimited number of lies or errors that seems to think much better than the human. Let us take an example of running the Anti-Mind algorithm to clarify what we mean by the 'algorithm thinks better than humans': CPC=Number of Correct Digits in Correct Position CPE=Number of Correct Digits in Incorrect Position, 3 Digits, Interval [0,3] 103 CPC,CPE=1,1 132 CPC,CPE=1,1 120 CPC,CPE=0,2, **Enough Information!**, Secret code=? The Anti-Mind algorithm knows that the information is enough, i.e. only one hypothesis remains, the secret code, but even people with lot of experience with this game have great difficulty in reaching the same conclusion. In this paper we will present an extension of this algorithm, the Anti-Mind with an unlimited number of lies which detects and identifies all guesses that have lies or errors and finds the secret code and we will present an example of running this algorithm with 6 lies and a secret code with 4 digits varying between 0 and 9. We will discuss, at the light of cognitive science, why no human would be capable of doing this apparently simple task. Then we present an exhaustive simulation for all possible secret codes with four digits varying between 0 and 9 and the number of lies varying between 1 and 7. As expected the average number of guesses increases with the number of lies or errors, shifting the successive histograms to the right. Finally we show how the Anti-Mind with Lies algorithm could be used as a starting point to develop a computational aid for the work of detectives in the analysis of noisy data where some pieces of noisy information must be excluded to reach a conclusion and there are many manners to remove the suspected noisy informations. In this sense our paper can be seen as a work in the line of the Strong AI Hypothesis where we try to imitate the human on complex problem solving tasks like a detective analysing a set of data where he must discover the subset that have lies or errors and the Truth.