An optimization statement consists of a set of elements consisting of a tuple together with a condition. Whenever the condition of such an element is true wrt an answer set, its associated tuple contributes a value to a set. Hence, if two equal tuples have true conditions, then only one value is provided. Additionally, tuples can have levels attached with the binary connective @ after the first tuple element - its value.

For example

1 { a; b }.
#minimize { 2,t:a; 2,t:b; 1,u:b; 2,v:b }.

Given answer set {a, b}, the values of tuples (2,t), (1,u), and (2,v) are summed up. Hence, the minimize constraint evaluates to 5. Note that the value of tuple (2,t) provided by the first and second element of the optimization constraint is counted only once.

Given (the optimal) answer set {a}, the only tuple is (2,t). Hence, the minimize constraint evaluates to 2.