A primer on Answer Set Programming

where A0, . . . An are atoms and not is a logical connective called negation as failure. Also, for every rule let us define head(ρ) = A0, pos(ρ) = A1, . . . , Am, neg(ρ) = Am+1, . . . , An and body(ρ) = pos(ρ)∪ neg(ρ). The head of rules is never empty, while if body(ρ) = ∅ we refer to ρ as a fact. A logic program is defined as a collection of rules. Rules with variables are taken as shorthand for the sets of all their ground instantiations and the set of all ground atoms in the language of a program Π will be denoted by IBΠ . Queries and constraints are expressions with the same structure of rules but with empty head.