Prolog (Programming in Logic) is one of the most well-known logic programming languages.
Mercury is a logic/functional programming language that combines logic programming with functional programming paradigms.
Datalog is a subset of Prolog and is often used for expressing queries and constraints in deductive databases.
ASP is a declarative programming paradigm used for solving knowledge representation and combinatorial optimization problems.
ECLiPSe (Embeddable CLP(i) System) is a software development platform for constraint logic programming.