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To see all available qualifiers, see our documentation.
Gödel http://en.wikipedia.org/wiki/G%C3%B6del_%28programming_language%29 http://www.scs.leeds.ac.uk/hill/GOEDEL/expgoedel.html
λProlog
Twelf (more of a proof checker, but can be used for logic programming)
Datalog (really a family of languages)
Answer Set Programming (really an approach rather than a specific language)