An Empirical Study of the 3 - Valued Kripke - Kleene

We empirically studied the behavior of the 3-Valued Kripke-Kleene semantics in a parameterized distribution of random propositional logic programs. In our distribution, programs with m rules are generated from n propositional letters by repeating the following process m times: uniformly, randomly, and independently choose k letters (with replacement) from the set of n proposition letters and negate each of the last k ? 1 letters independently with probability p. The rst letter becomes the head of the rule and the remaining k ? 1 literals become the subgoals. The collection of m rules make up the logic program. We xed p = 0:5, k = 3 and varied n over a range of values investigating, for each, the relationship between m=n and the percentage of inconsistent models produced by the 3-Valued Kripke-Kleene semantics. In all of our experiments, the 3-Valued Kripke-Kleene semantics were computed with respect to a xed percentage of proposition letters (randomly chosen) initially assigned TRUE and a xed percentage (randomly chosen) initially assigned FALSE. We observed that there exist regions in the parameter space of our distribution in which the 3-Valued Kripke-Kleene semantics tends to produce a high percentage of inconsistent models, therefore, providing information useful to prune branches in a backtracking search for stable models. Also, we observed a region in which a very small percentage of inconsistent models are produced, therefore, providing very little information useful for pruning branches in a backtracking search.