[nrub]

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.

[seanmcdirmid]

Its also not that hard to build a backward (prolog) or forward (datalog) chaining predicate rule system in whatever your favorite language is; as a bonus, you'll get to learn the joys of unification, or go crazy with some higher order predicates.

Once you get bored with unification, then look at dealing with inequalities and learn some constraint solving. Prolog and datalog look quite simplistic compared to some of the more developed logics out there.