Forward Human Reasoning Modeled by Logic Programming Modeled by Classical Logic with Circumscription and Projection

Recently an approach to model human reasoning as studied in cognitive science by logic programming, has been introduced by Stenning and van Lambalgen and exemplified with the suppression task. We investigate this approach from the view of a framework where different logic programming semantics correspond to different translations of logic programs into formulas of classical two-valued logic extended by two second-order operators, circumscription and literal projection. Based on combining and extending previously known such renderings of logic programming semantics, we take semantics into account that have not yet been considered in the context of human reasoning, such as stable models and partial stable models. To model human reasoning, it is essential that only some predicates can be subjected to closed world reasoning, while others are handled by open world reasoning. In our framework, variants of familiar logic programing semantics that are extended with this feature are derived from a generic circumscription based representation. Further, we develop a two-valued representation of a three-valued logic that renders semantics considered for human reasoning based on the Fitting operator.