Reducing Propositional Theories in Equilibrium Logic to Logic Programs

Abstract

The paper studies reductions of propositional theories in equilibrium logic to logic programs under answer set semantics. Specifically we are concerned with the question of how to transform an arbitrary set of propositional formulas into an equivalent logic program and what are the complexity constraints on this process. We want the transformed program to be equivalent in a strong sense so that theory parts can be transformed independent of the wider context in which they might be embedded. It was only recently established [1] that propositional theories are indeed equivalent (in a strong sense) to logic programs. Here this result is extended with the following contributions. (i) We show how to effectively obtain an equivalent program starting from an arbitrary theory. (ii) We show that in general there is no polynomial time transformation if we require the resulting program to share precisely the vocabulary or signature of the initial theory. (iii) Extending previous work we show how polynomial transformations can be achieved if one allows the resulting program to contain new atoms. The program obtained is still in a strong sense equivalent to the original theory, and the answer sets of the theory can be retrieved from it.