Answer Sets and the Language of Answer Set Programming

Its main ideas are described in the article by Janhunen and Niemelä (2016) and in other contributions to this special issue. In this introductory article my goal is to discuss the concept of an answer set, or stable model, which defines the semantics of ASP languages. The answer sets of a logic program are sets of atomic formulas without variables ("ground atoms"), and they were introduced in the course of research on the semantics of negation in Prolog. For this reason, I will start with examples illustrating the relationship between answer sets and Prolog and the relationship between answer set solvers and Prolog systems. Then I will review the mathematical definition of an answer set and discuss some extensions of the basic language of ASP.