We consider the problem of obtaining a minimal logic program strongly equivalent (under the stable models semantics) to a
given arbitrary propositional theory. We propose a method consisting in the generation of the set of prime implicates of the
original theory, starting from its set of countermodels (in the logic of Here-and-There), in a similar vein to the Quine-McCluskey
method for minimisation of boolean functions. As a side result, we also provide several results about fundamental rules (those that are not tautologies and do not contain redundant literals) which are combined to build the minimal programs.
In particular, we characterise their form, their corresponding sets of countermodels, as well as necessary and sufficient
conditions for entailment and equivalence among them.
Keywords logic programming - answer set programming - minimisation of boolean and multivalued functions