A major goal of the Human Genome Project is to construct detailed physical maps of the human genome. A physical map is an assignment of DNA fragments to their locations on the genome. Complete maps of large genomes require the integration of many kinds of experimental data, each with its own forms of noise and experimental error. To facilitate this integration, we are developing a flexible approach to map assembly based on logic programming and data visualization. Logic programming provides a convenient and mathematically rigorous way of reasoning about data, while data visualization provides layout algorithms for assembling and displaying genome maps. To demonstrate the approach, this paper describes numerous rules for map assembly implemented in a data-visualization system called Hy+. Using these rules, we have successfully assembled contigs (partial maps) from real and simulated mapping data---data that is noisy, imprecise and contradictory. The main advantage of the approach is that it allows a user to rapidly develop, implement and test new rules for genome map assembly, with a minimum of programming effort.