Landmine detection can be cast as a model selection problem in which probability theory is used as logic for inductive inference. Using this method, the landmine detection decision is based on the values of calculated posterior probabilities for two propositions: 'The received signal is from a landmine' and 'The received signal is from the background.' The posterior probability for a proposition is the probability for the proposition given the observed data signal and the information known prior to the observation. Calculation of the posterior probability requires the numerical integration of a multi-dimensional probability density function. Until the beginning of the last decade, there were few robust methods available to perform these numeral integrations and no methods that could be generally applied. As a result, probability theory as logic for inductive inference found only infrequent use in practical detection algorithms. Because of the increasing power of computers and new research in the areas of Markov chain Monte Carlo and multi-dimensional adaptive-quadrature integration methods, practical detection algorithms based on the use of probability theory as logic for inductive inference are now being developed and used. This paper describes our model selection formulation of the landmine detection problem and presents results obtained using multi-dimensional adaptive quadrature.