In the context of a Java/Eclipse application I would like to use Prolog for a particular task. What are the available solutions and tools to do that, and associated pro and
A quick google returns a list of options (alas not updated in 5 years).
As for pros/cons - as I see it
Native engine with bindings would be the worse option when it comes to distribution and integration, but may be faster than the native Java engines (but I would want proof first).
Java engine with API would lead to some awkwardness at integration points, but should be easy to distribute.
Prolog to bytecode compiler should handle integration between the two languages nicely, and would mean that you are not shipping prolog scripts with the binary (may be a disadvantage). Big disadvantage with this - none still seem to be a live.
Prolog-alike language to bytecode compiler, same as above, but some still seem to be floating about, also would require knowledge of a new language.
Java rules engine - I'd see this as the neatest solution. Rather than use two languages code the rules in a Java-y way, but it depends on how complicated the rules are to express in that way.
A second thing to consider is - is the project still being updated. From my quick google, few are. Prova and Mandarax are two exceptions from the latter options.