We investigate the potential of logic programming (LP) to computationally model morality aspects studied in philosophy and psychology. We do so by identifying threemorality aspects that appear in our view amenable to computational modeling by appropriately exploiting LP features: dual-process model (reactive and deliberative) in moral judgment, justification of moral judgments by contractualism, and intention in moral permissibility. The research aims at developing an LP-based system with features needed in modeling moral settings, putting emphasis on modeling these abovementioned morality aspects. We have currently co-developed two essential ingredients of the LP system, i.e., abduction and logic program updates, by exploiting the benefits of tabling features in logic programs. They serve as the basis for our whole system, into which other reasoning facets will be integrated, to model the surmised morality aspects. We exemplify two applications pertaining moral updating and moral reasoning under uncertainty and detail their implementation. Moreover,we touch upon the potential of our ongoing studies of LP-based cognitive features for the emergence of computational morality, in populations of agents enabled with the capacity for intention recognition, commitment, and apology. We conclude with a “message in a bottle” pertaining to this bridging of individual and population computational morality via cognitive abilities.