  Logic regression was developed more than a decade ago as a tool to construct
predictors from Boolean combinations of binary covariates. It has been mainly
used to model epistatic effects in genetic association studies, which is very
appealing due to the intuitive interpretation of logic expressions to describe
the interaction between genetic variations. Nevertheless logic regression has
(partly due to computational challenges) remained less well known than other
approaches to epistatic association mapping. Here we will adapt an advanced
evolutionary algorithm called GMJMCMC (Genetically modified Mode Jumping Markov
Chain Monte Carlo) to perform Bayesian model selection in the space of logic
regression models. After describing the algorithmic details of GMJMCMC we
perform a comprehensive simulation study that illustrates its performance given
logic regression terms of various complexity. Specifically GMJMCMC is shown to
be able to identify three-way and even four-way interactions with relatively
large power, a level of complexity which has not been achieved by previous
implementations of logic regression. We apply GMJMCMC to reanalyze QTL mapping
data for Recombinant Inbred Lines in \textit{Arabidopsis thaliana} and from a
backcross population in \textit{Drosophila} where we identify several
interesting epistatic effects. The method is implemented in an R package which
is available on github.
