The abductive logic program below describes a simple model of the lactose metabolism of the bacterium E. coli. The program, ''P'', describes (in its first rule) that E. coli can feed on the sugar lactose if it makes two enzymes permease and galactosidase. Like all enzymes (E), these are made if they are coded by a gene (GGene) that is expressed (described by the second rule). TheseThe two enzymes of permease and galactosidase are coded by two genes, (lac(y) and lac(z) respectively (stated in the fifth and sixth rule of the program), in a cluster of genes (lac(X)) – called an operon – that is expressed when the amounts (amt) of glucose are low and lactose are high or when they are both at medium level (see the fourth and fifth rule). The abducibles, ''A'', declare all ground instances of the predicates "amount" as assumable. This reflects that in the model the amounts at any time of the various substances are unknown. This is incomplete information that is to be determined in each problem case.
The integrity constraints, ''IC'', state that the amount of aany substance (S) can only take one value.
