Check out Datalog the query language used to interact with Datomic, www.learndatalogtoday.org

William Byrd & Daniel Friedman wrote a book called the Reasoned Schemer, which walks through the implementation of a Prolog like logic language called MiniKanren, check out a recent presentation they gave where they show quite a few interesting examples and uses, http://2013.flatmap.no/danwill.html

I know this is not a definitive answer, but having a look at those resources may highlight some of the areas where logic programming can be very useful.