# Fixpoint Characterizations for Many−Valued Disjunctive Logic Programs with Probabilistic Semantics

*Thomas Lukasiewicz*

### Abstract

In this paper, we continue to explore many-valued disjunctive logic programs with probabilistic semantics. In particular, we newly introduce the least model state semantics for such programs. We show that many-valued disjunctive logic programs under the semantics of minimal models, perfect models, stable models, and least model states can be unfolded to equivalent classical disjunctive logic programs under the respective semantics. Thus, existing technology for classical disjunctive logic programming can be used to implement many-valued disjunctive logic programming. Using these results on unfolding many-valuedness, we then give many-valued fixpoint characterizations for the set of all minimal models and the least model state. We also describe an iterative fixpoint characterization for the perfect model semantics under finite local stratification.